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Strong $P$-cleanness of trivial Morita contexts

Abdullah Harmanci|Sait Halicioglu|Mete B. Calci
대한수학회 (The Korean Mathematical Society)|2019.10|대한수학회논문집 (Communications of the KMS)|제34권 제4호|pp. 1069-1078|DOI 10.4134/CKMS.c180361

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키워드

Morita contextprime radicalstrongly $P$-clean ringstrongly clean ringtriangular matrix ring
주제분류수학

초록

Let $R$ be a ring with identity and $P(R)$ denote the prime radical of $R$. An element $r$ of a ring $R$ is called strongly $P$-clean, if there exists an idempotent $e$ such that $r-e=p \in P(R)$ with $ep=pe$. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly $P$-clean.

Abstract

Let $R$ be a ring with identity and $P(R)$ denote the prime radical of $R$. An element $r$ of a ring $R$ is called strongly $P$-clean, if there exists an idempotent $e$ such that $r-e=p \in P(R)$ with $ep=pe$. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly $P$-clean.

참고문헌 (16)

  1. Gautam Borooah, "Strongly clean triangular matrix rings over local rings", Journal of Algebra, 312(2), pp.773~797 (2007), Elsevier BV[DOI]
  2. Gautam Borooah, "Strongly clean matrix rings over commutative local rings", Journal of Pure and Applied Algebra, 212(1), pp.281~296 (2008), Elsevier BV[DOI]
  3. "Prime Structures in a Morita Context"[URL]
  4. Huanyin Chen, "ON 2 × 2 STRONGLY CLEAN MATRICES", 대한수학회보, 50(1), pp.125~134 (2013), 대한수학회
  5. Huanyin Chen, "STRONGLY P-CLEAN RINGS AND MATRICES", International Electronic Journal of Algebra, 15(15), pp.116~116 (2014), The International Electronic Journal of Algebra[DOI]
  6. Jianlong Chen, "When is the 2×2 matrix ring over a commutative local ring strongly clean?", Journal of Algebra, 301(1), pp.280~293 (2006), Elsevier BV[DOI]
  7. Jianlong Chen, "On Strongly Clean Matrix and Triangular Matrix Rings", Communications in Algebra, 34(10), pp.3659~3674 (2007), Informa UK Limited[DOI]
  8. Alexander J. Diesl, "Nil clean rings", Journal of Algebra, 383, pp.197~211 (2013), Elsevier BV[DOI]
  9. Irving Kaplansky, "Topological Representation of Algebras. II", Transactions of the American Mathematical Society, 68(1), pp.62~ (1950), JSTOR[DOI]
  10. Yuanlin Li, "Strongly clean matrix rings over local rings", Journal of Algebra, 312(1), pp.397~404 (2007), Elsevier BV[DOI]
  11. K. Morita, "Duality for modules and its applications to the theory of rings with minimum condition", Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 6, pp.83~142 (1958)
  12. Müller Marianne, "Rings of quotients of generalized matrix rings", Communications in Algebra, 15(10), pp.1991~2015 (1987), Informa UK Limited[DOI]
  13. W. K. Nicholson, "Strongly clean rings and fitting's lemma", Communications in Algebra, 27(8), pp.3583~3592 (1999), Informa UK Limited[DOI]
  14. Guangtian Song, "Diagonability of idempotent matrices over noncommutative rings", Linear Algebra and its Applications, 297(1-3), pp.1~7 (1999), Elsevier BV[DOI]
  15. Gaohua Tang, "Study of Morita contexts", Communications in Algebra, 42(4), pp.1668~1681 (2013), Informa UK Limited[DOI]
  16. Gaohua Tang, "Strong cleanness of generalized matrix rings over a local ring", Linear Algebra and its Applications, 437(10), pp.2546~2559 (2012), Elsevier BV[DOI]

관련 논문AI추천

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