{"id":41008,"date":"2024-09-25T10:28:56","date_gmt":"2024-09-25T10:28:56","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c-%d8%b1%d8%a7%d8%a8%d8%b7%d9%87-%d8%a7%db%8c%d8%af\/"},"modified":"2024-09-25T10:28:57","modified_gmt":"2024-09-25T10:28:57","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c-%d8%b1%d8%a7%d8%a8%d8%b7%d9%87-%d8%a7%db%8c%d8%af","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c-%d8%b1%d8%a7%d8%a8%d8%b7%d9%87-%d8%a7%db%8c%d8%af\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0628\u0627\u0644\u0627\u06cc\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u062d\u0644\u0642\u0647 \u0647\u0627"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nUpper ideal relation graphs associated to rings<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0628\u0627\u0644\u0627\u06cc\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u062d\u0644\u0642\u0647 \u0647\u0627<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nBarkha Baloda, Jitender Kumar<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n16<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nRings and Algebras,Combinatorics,\u062d\u0644\u0642\u0647 \u0647\u0627 \u0648 \u062c\u0628\u0631 \u0647\u0627 , \u062a\u0631\u06a9\u06cc\u0628\u0627\u062a ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 7 March, 2024; originally announced March 2024. , MSC Class: 05C25<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 7 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u06a9\u0644\u0627\u0633 MSC: 05C25<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Let $R$ be a ring with unity. The upper ideal relation graph $\u0393_U(R)$ of the ring $R$ is a simple undirected graph whose vertex set is the set of all non-unit elements of $R$ and two distinct vertices $x, y$ are adjacent if and only if there exists a non-unit element $z \\in R$ such that the ideals $(x)$ and $(y)$ contained in the ideal $(z)$. In this article, we classify all the non-local finite commutative rings whose upper ideal relation graphs are split graphs, threshold graphs and cographs, respectively. In order to study topological properties of $\u0393_U(R)$, we determine all the non-local finite commutative rings $R$ whose upper ideal relation graph has genus at most $2$. Further, we precisely characterize all the non-local finite commutative rings for which the crosscap of $\u0393_U(R)$ is either $1$ or $2$.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0628\u06af\u0630\u0627\u0631\u06cc\u062f $ r $ \u062d\u0644\u0642\u0647 \u0627\u06cc \u0628\u0627 \u0648\u062d\u062f\u062a \u0628\u0627\u0634\u062f.\u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0641\u0648\u0642\u0627\u0646\u06cc $ \u03b3_u (r) $ \u062d\u0644\u0642\u0647 $ r $ \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0633\u0627\u062f\u0647 \u0628\u062f\u0648\u0646 \u06a9\u0627\u0631\u06af\u0631\u062f\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0631\u0627\u0633 \u0622\u0646 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u0647\u0645\u0647 \u0639\u0646\u0627\u0635\u0631 \u063a\u06cc\u0631 \u0648\u0627\u062d\u062f\u06cc $ R $ \u0648 \u062f\u0648 \u0631\u0627\u0633 \u0645\u062c\u0632\u0627 $ x \u0627\u0633\u062a \u060c y $ \u062f\u0631 \u0635\u0648\u0631\u062a \u0645\u062c\u0627\u0648\u0631 \u0627\u0633\u062a\u0648 \u062a\u0646\u0647\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a \u0648\u062c\u0648\u062f \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u063a\u06cc\u0631 \u0648\u0627\u062d\u062f\u06cc $ z \\ \u062f\u0631 r $ \u0628\u0647 \u06af\u0648\u0646\u0647 \u0627\u06cc \u06a9\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0647\u0627\u06cc $ (x) $ \u0648 $ (y) $ \u0645\u0648\u062c\u0648\u062f \u062f\u0631 $ $ (Z) $ \u0628\u0627\u0634\u062f.\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u060c \u0645\u0627 \u062a\u0645\u0627\u0645 \u062d\u0644\u0642\u0647 \u0647\u0627\u06cc \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u0645\u062d\u062f\u0648\u062f \u063a\u06cc\u0631 \u0645\u062d\u0644\u06cc \u0631\u0627 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0641\u0648\u0642\u0627\u0646\u06cc \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u062a\u0642\u0633\u06cc\u0645 \u060c \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0622\u0633\u062a\u0627\u0646\u0647 \u0648 \u06a9\u0648\u06af\u0631\u0627\u0641\u06cc \u0647\u0627 \u0647\u0633\u062a\u0646\u062f.\u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u0645\u0637\u0627\u0644\u0639\u0647 \u062e\u0648\u0627\u0635 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc $ \u03b3_u (r) $ \u060c \u0645\u0627 \u062a\u0645\u0627\u0645 \u062d\u0644\u0642\u0647 \u0647\u0627\u06cc \u0631\u0641\u062a \u0648 \u0622\u0645\u062f \u0645\u062d\u062f\u0648\u062f \u063a\u06cc\u0631 \u0645\u062d\u0644\u06cc $ R $ \u0631\u0627 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc\u062f\u0647 \u0622\u0644 \u0641\u0648\u0642\u0627\u0646\u06cc \u062f\u0627\u0631\u0627\u06cc \u062c\u0646\u0633 \u062d\u062f\u0627\u06a9\u062b\u0631 2 \u062f\u0644\u0627\u0631 \u0627\u0633\u062a.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0645\u0627 \u062f\u0642\u06cc\u0642\u0627\u064b \u062a\u0645\u0627\u0645 \u062d\u0644\u0642\u0647 \u0647\u0627\u06cc \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u0645\u062d\u062f\u0648\u062f \u063a\u06cc\u0631 \u0645\u062d\u0644\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0635\u0644\u06cc\u0628 $ \u03b3_u (r) $ $ 1 \u062f\u0644\u0627\u0631 \u06cc\u0627 2 \u062f\u0644\u0627\u0631 \u0627\u0633\u062a \u060c \u062a\u0648\u0635\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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