Matrix rings over a principal ideal domain in which elements are nil-clean
نویسندگان
چکیده
منابع مشابه
On the nil-clean matrix over a UFD
In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix over a UFD is nil-clean.
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We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings, then $R/J(R)$ is nil-clean. In particular, under certain additional circumstances, $R$ is also nil-clean. These results somewhat improves on achievements due to Diesl in J. Algebra (2013) and to Koc{s}an-Wang-Zhou in J. Pure Appl. Algebra (2016). ...
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In [5] and [6], a nil clean ring was defined as a ring for which every element is the sum of a nilpotent and an idempotent. In this short article we characterize nil clean commutative group rings.
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A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...
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The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual...
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ژورنال
عنوان ژورنال: Journal of Algebra Combinatorics Discrete Structures and Applications
سال: 2016
ISSN: 2148-838X
DOI: 10.13069/jacodesmath.82415