\u0645\u0646\u0627\u0642\u0634\u0629 \u0631\u0633\u0627\u0644\u0629 \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>N- idempotent divisors graph of commutative rings<\/strong>“<\/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\u0627\u062d\u062f \u0627\u0644\u0645\u0648\u0627\u0641\u0642 10-<\/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\u0628\u0627\u0633 \u062d\u0633\u0646 \u0645\u0633\u0637\u0648 \u0634\u064a\u062e\u0648 <\/strong>\u0648\u0628\u0625\u0634\u0631\u0627\u0641 \u0627\u0644\u0623\u0633\u062a\u0627\u0630 \u0627\u0644\u062f\u0643\u062a\u0648\u0631<\/strong> \u062d\u0633\u0627\u0645 \u0642\u0627\u0633\u0645 \u0645\u062d\u0645\u062f <\/strong>.<\/strong><\/p>\n \u0644\u062a\u0643\u0646 R\u00a0 \u062d\u0644\u0642\u0629 \u062a\u0628\u062f\u064a\u0644\u064a\u0629 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0639\u0646\u0627\u0635\u0631 \u0645\u062d\u0627\u064a\u062f\u0629 1\u22600 . \u064a\u064f\u0639\u0631\u0651\u0641 \u0631\u0633\u0645 \u0627\u0644\u0642\u0648\u0627\u0633\u0645 \u0627\u0644\u0623\u064a\u062f\u064a\u0645\u0628\u0648\u062a\u0646\u062a\u064a\u0629 \u0641\u064a R\u00a0 \u0628\u0623\u0646\u0647 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u0628\u0633\u064a\u0637 \u03a0( R ) \u0627\u0644\u0630\u064a \u062a\u0643\u0648\u0646 \u0631\u0624\u0648\u0633\u0647 \u0647\u064a \u0639\u0646\u0627\u0635\u0631 R \u060c \u0648\u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0636\u0644\u0639 \u0628\u064a\u0646 \u0627\u0644\u0639\u0646\u0635\u0631\u064a\u0646 a \u0648 b \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 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\u0644\u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u062a\u0633\u0627\u0648\u064a \u03a0_n (R)=\u03a0_m (R) \u062d\u064a\u062b n\u2260m .<\/p>\n \u062a\u0631\u0623\u0633 \u0644\u062c\u0646\u0629 \u0627\u0644\u0645\u0646\u0627\u0642\u0634\u0629 <\/strong>\u0623.\u062f. \u0646\u0632\u0627\u0631 \u062d\u0645\u062f\u0648\u0646 \u0634\u0643\u0631 <\/strong><\/p>\n <\/p>\n \u0648\u0639\u0636\u0648\u064a\u0629 \u0643\u0644 \u0645\u0646 :<\/strong><\/p>\n \u0623.\u062f. \u0627\u062d\u0645\u062f \u0645\u062d\u0645\u062f \u0639\u0644\u064a<\/strong> \/ \u0639\u0636\u0648\u0627\u064b <\/strong><\/p>\n \u0627.\u0645.\u062f. \u0628\u0631\u0627\u0621\u0629 \u0645\u062d\u0645\u0648\u062f \u0633\u0644\u064a\u0645\u0627\u0646 \/ \u0639\u0636\u0648\u0627\u064b<\/strong><\/p>\n \u0623.\u062f. \u062d\u0633\u0627\u0645 \u0642\u0627\u0633\u0645 \u0645\u062d\u0645\u062f \/ \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 \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 : ” N- idempotent divisors graph of commutative rings“ \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\u0627\u062d\u062f \u0627\u0644\u0645\u0648\u0627\u0641\u0642 10-8–2025 \u0631\u0633\u0627\u0644\u0629 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\u062a\u0643\u0648\u0646 \u0631\u0624\u0648\u0633\u0647 \u0647\u064a \u0639\u0646\u0627\u0635\u0631 R \u060c \u0648\u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0636\u0644\u0639 \u0628\u064a\u0646 \u0627\u0644\u0639\u0646\u0635\u0631\u064a\u0646 a \u0648 b \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 \u0625\u0630\u0627 \u062a\u062d\u0642\u0642 ab=e \u060c \u062d\u064a\u062b e \u0639\u0646\u0635\u0631 \u0622\u064a\u062f\u064a\u0645\u0628\u0648\u062a\u0646\u062a (\u0623\u064a e^2=e\u00a0 [\u0625\u0642\u0631\u0623 \u0627\u0644\u0645\u0632\u064a\u062f]<\/a><\/p>\n","protected":false},"author":20,"featured_media":45045,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-45044","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\/45044","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=45044"}],"version-history":[{"count":1,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts\/45044\/revisions"}],"predecessor-version":[{"id":45046,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/posts\/45044\/revisions\/45046"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/media\/45045"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/media?parent=45044"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/categories?post=45044"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/computerscience\/wp-json\/wp\/v2\/tags?post=45044"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}