\u0645\u0646\u0627\u0642\u0634\u0629 \u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0641\u064a \u0643\u0644\u064a\u0629 \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a – \u0642\u0633\u0645 \u0639\u0644\u0648\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0628\u0639\u0646\u0648\u0627\u0646 :<\/p>\n
“<\/strong> \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u0646\u0642\u064a\u0629 \u0627\u0644\u0645\u0639\u062f\u0648\u0645\u0629 \u0627\u0644\u062e\u0645\u0627\u0633\u064a\u0629”<\/strong><\/p>\n \u201c5- Potent Nil Clean Rings\u201d<\/strong><\/p>\n \u0646\u0648\u0642\u0634\u062a \u0641\u064a \u0642\u0627\u0639\u0629 \u0627\u0644\u0645\u0646\u0627\u0642\u0634\u0629 \u0628\u0643\u0644\u064a\u0629 \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0645\u0648\u0635\u0644 \u064a\u0648\u0645 \u0627\u0644\u062e\u0645\u064a\u0633<\/strong> \u0627\u0644\u0645\u0648\u0627\u0641\u0642 2<\/strong>8-<\/strong>8<\/strong>–<\/strong>2025<\/strong><\/p>\n \u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0644\u0644\u0637\u0627\u0644\u0628<\/strong> \u0639\u0644\u064a \u062e\u0627\u0644\u062f \u0639\u0628\u0648 \u0645\u0637\u0631\u0648\u062f\u00a0<\/strong>\u0648\u0628\u0625\u0634\u0631\u0627\u0641 \u0627\u0644\u0623\u0633\u062a\u0627\u0630 \u0627\u0644\u062f\u0643\u062a\u0648\u0631<\/strong> \u0646\u0632\u0627\u0631 \u062d\u0645\u062f\u0648\u0646 \u0634\u0643\u0631<\/strong><\/p>\n \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647\u0627 \u062a\u0639\u0645\u064a\u0645\u0627\u064b \u0644\u0644\u062d\u0644\u0642\u0627\u062a \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0642\u0648\u0629 (Tripotent Rings) \u0637\u064f\u0631\u062d\u062a \u0641\u0643\u0631\u0629 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u062e\u0645\u0627\u0633\u064a\u0629 \u0627\u0644\u0642\u0648\u0629 (Five Potent Rings) \u0648\u0647\u064a \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u062d\u0642\u0642 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0641\u064a\u0647\u0627 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629. \u00a0\u064a\u0645\u062b\u0651\u0644 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0645\u0646\u0638\u0648\u0631\u064b\u0627 \u062c\u062f\u064a\u062f\u064b\u0627 \u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645\u062a\u0644\u0643 \u062e\u0635\u0627\u0626\u0635 \u062e\u0627\u0635\u0629 \u062a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0642\u0648\u0649\u060c \u062d\u064a\u062b \u062a\u0646\u0627\u0648\u0644\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0628\u0639\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u062d\u0644\u0642\u0627\u062a\u060c \u0645\u062b\u0644 \u0633\u0644\u0648\u0643 \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u062a\u062d\u062a \u0639\u0645\u0644\u064a\u062a\u064a \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0636\u0631\u0628\u060c \u0648\u0639\u0644\u0627\u0642\u062a\u0647\u0627 \u0628\u0623\u0646\u0648\u0627\u0639 \u062e\u0627\u0635\u0629 \u0645\u0646 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0645\u062b\u0644 \u0627\u0644\u0639\u0646\u0627\u0635\u0650\u0631 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 (Idempotents) \u0648\u0627\u0644\u0639\u0646\u0627\u0635\u0650\u0631 \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0639\u0643\u0633 (Units).<\/p>\n \u0643\u0645\u0627 \u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0646\u0648\u0639 \u062c\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0623\u064f\u0637\u0644\u0642 \u0639\u0644\u064a\u0647 \u0627\u0633\u0645 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u062e\u0645\u0627\u0633\u064a\u0629 \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0646\u0638\u064a\u0641\u0629 \u0627\u0644\u0639\u062f\u064a\u0645\u0629 (Five-Potent Nil Clean Rings) \u0623\u0648 \u0627\u062e\u062a\u0635\u0627\u0631\u064b\u0627 5-PNC Rings<\/strong> .<\/strong><\/p>\n \u0648\u0647\u064a \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0641\u064a\u0647\u0627 \u0643\u062a\u0627\u0628\u0629 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0639\u0644\u0649 \u0634\u0643\u0644 \u0645\u062c\u0645\u0648\u0639 \u0639\u0646\u0635\u0631 \u062e\u0645\u0627\u0633\u064a \u0627\u0644\u0642\u0648\u0629 \u0648\u0639\u0646\u0635\u0631 \u0639\u062f\u064a\u0645 (Nilpotent) \u064a\u0635\u0628\u062d \u0635\u0641\u0631\u064b\u0627 \u0639\u0646\u062f \u0631\u0641\u0639\u0647 \u0644\u0642\u0648\u0629 \u0645\u0639\u064a\u0646\u0629. \u0648\u064a\u064f\u0639\u062f \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u062a\u0639\u0645\u064a\u0645\u064b\u0627 \u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u0646\u0638\u064a\u0641\u0629 \u0627\u0644\u0639\u062f\u064a\u0645\u0629 (Nil Clean Rings) \u0627\u0644\u062a\u0642\u0644\u064a\u062f\u064a\u0629<\/p>\n \u0648\u0642\u062f \u062c\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0628\u062d\u062b \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u062d\u0644\u0642\u0627\u062a 5-PNC<\/strong> \u0648\u0623\u0646\u0648\u0627\u0639 \u0623\u062e\u0631\u0649 \u0645\u0646 \u0627\u0644\u062d\u0644\u0642\u0627\u062a\u060c \u0645\u062b\u0644 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u0646\u0638\u064a\u0641\u0629 \u0627\u0644\u0639\u062f\u064a\u0645\u0629\u060c \u0648\u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u0646\u0638\u064a\u0641\u0629 \u0627\u0644\u0639\u062f\u064a\u0645\u0629 \u0627\u0644\u0642\u0648\u064a\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 (Strongly 2-Nil Clean Rings) \u0648\u0627\u0644\u062d\u0644\u0642\u0627\u062a \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0642\u0648\u0629\u060c \u0645\u0639 \u0628\u064a\u0627\u0646 \u0623\u0648\u062c\u0647 \u0627\u0644\u062a\u0634\u0627\u0628\u0647 \u0648\u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641 \u0628\u064a\u0646\u0647\u0627\u060c \u0648\u062a\u0642\u062f\u064a\u0645 \u0628\u0639\u0636 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0628\u0646\u064a\u062a\u0647\u0627.<\/p>\n \u062a\u064f\u0633\u0647\u0645 \u0647\u0630\u0647 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u062c\u062f\u064a\u062f\u0629 \u0641\u064a \u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0641\u0647\u0645 \u0627\u0644\u0646\u0638\u0631\u064a \u0644\u0644\u062d\u0644\u0642\u0627\u062a\u060c \u0648\u0642\u062f \u062a\u0645\u0647\u0651\u062f \u0627\u0644\u0637\u0631\u064a\u0642 \u0644\u0625\u062c\u0631\u0627\u0621 \u062f\u0631\u0627\u0633\u0627\u062a \u062c\u062f\u064a\u062f\u0629 \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062c\u0628\u0631 \u0648\u0641\u0631\u0648\u0639 \u0623\u062e\u0631\u0649 \u0645\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a<\/p>\n \u062a\u0631\u0623\u0633 \u0644\u062c\u0646\u0629 \u0627\u0644\u0645\u0646\u0627\u0642\u0634\u0629 <\/strong>\u0623.\u062f. \u0623\u0643\u0631\u0645 \u0633\u0627\u0644\u0645 \u0645\u062d\u0645\u062f<\/strong><\/p>\n \u0648\u0639\u0636\u0648\u064a\u0629 \u0643\u0644 \u0645\u0646 :<\/strong><\/p>\n \u0623.\u062f. \u0646\u062f\u0649 \u064a\u0627\u0633\u064a\u0646 \u0642\u0627\u0633\u0645 \/ \u0639\u0636\u0648\u0627\u064b<\/strong><\/p>\n \u00a0<\/strong>\u0623.\u0645. \u0627\u0643\u0631\u0627\u0645 \u0639\u0628\u062f \u0627\u0644\u0642\u0627\u062f\u0631 \u0635\u0627\u0644\u062d \/ \u0639\u0636\u0648\u0627\u064b<\/strong><\/p>\n \u00a0\u0623.\u062f. \u0646\u0632\u0627\u0631 \u062d\u0645\u062f\u0648\u0646 \u0634\u0643\u0631 \/ \u0639\u0636\u0648\u0627\u064b \u0648\u0645\u0634\u0631\u0641\u0627\u064b<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" \u0645\u0646\u0627\u0642\u0634\u0629 \u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0641\u064a \u0643\u0644\u064a\u0629 \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a – \u0642\u0633\u0645 \u0639\u0644\u0648\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0628\u0639\u0646\u0648\u0627\u0646 : “ \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u0646\u0642\u064a\u0629 \u0627\u0644\u0645\u0639\u062f\u0648\u0645\u0629 \u0627\u0644\u062e\u0645\u0627\u0633\u064a\u0629” \u201c5- Potent Nil Clean Rings\u201d \u0646\u0648\u0642\u0634\u062a \u0641\u064a \u0642\u0627\u0639\u0629 \u0627\u0644\u0645\u0646\u0627\u0642\u0634\u0629 \u0628\u0643\u0644\u064a\u0629 \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u0645\u0648\u0635\u0644 \u064a\u0648\u0645 \u0627\u0644\u062e\u0645\u064a\u0633 \u0627\u0644\u0645\u0648\u0627\u0641\u0642 28-8–2025 \u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0644\u0644\u0637\u0627\u0644\u0628 \u0639\u0644\u064a \u062e\u0627\u0644\u062f \u0639\u0628\u0648 \u0645\u0637\u0631\u0648\u062f\u00a0\u0648\u0628\u0625\u0634\u0631\u0627\u0641 \u0627\u0644\u0623\u0633\u062a\u0627\u0630 \u0627\u0644\u062f\u0643\u062a\u0648\u0631 \u0646\u0632\u0627\u0631 \u062d\u0645\u062f\u0648\u0646 \u0634\u0643\u0631 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647\u0627 \u062a\u0639\u0645\u064a\u0645\u0627\u064b \u0644\u0644\u062d\u0644\u0642\u0627\u062a \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0642\u0648\u0629 (Tripotent Rings) \u0637\u064f\u0631\u062d\u062a \u0641\u0643\u0631\u0629 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u062e\u0645\u0627\u0633\u064a\u0629 \u0627\u0644\u0642\u0648\u0629 (Five Potent Rings) \u0648\u0647\u064a \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u062d\u0642\u0642 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0641\u064a\u0647\u0627 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629. \u00a0\u064a\u0645\u062b\u0651\u0644 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0645\u0646\u0638\u0648\u0631\u064b\u0627 \u062c\u062f\u064a\u062f\u064b\u0627 \u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u0644\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645\u062a\u0644\u0643 \u062e\u0635\u0627\u0626\u0635 \u062e\u0627\u0635\u0629 \u062a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0642\u0648\u0649\u060c \u062d\u064a\u062b \u062a\u0646\u0627\u0648\u0644\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0628\u0639\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u062d\u0644\u0642\u0627\u062a\u060c \u0645\u062b\u0644 \u0633\u0644\u0648\u0643 \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u062a\u062d\u062a \u0639\u0645\u0644\u064a\u062a\u064a \u0627\u0644\u062c\u0645\u0639 [\u0625\u0642\u0631\u0623 \u0627\u0644\u0645\u0632\u064a\u062f]<\/a><\/p>\n","protected":false},"author":20,"featured_media":45080,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-45079","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts\/45079","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/comments?post=45079"}],"version-history":[{"count":1,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts\/45079\/revisions"}],"predecessor-version":[{"id":45081,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts\/45079\/revisions\/45081"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/media\/45080"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/media?parent=45079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/categories?post=45079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/tags?post=45079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}