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On the Genus of the Co-Annihilating Graph of Commutative Rings
Discussiones Mathematicae - General Algebra and Applications, 2019 Let R be a commutative ring with identity and 𝒰R be the set of all nonzero non-units of R. The co-annihilating graph of R, denoted by 𝒞𝒜R, is a graph with vertex set 𝒰R and two vertices x and y are adjacent whenever ann(x) ∩ ann(y) = (0).
Selvakumar K., Karthik S.
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Hopfian additive groups of rings [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаA group is called Hopfian if it is not isomorphic to any of its proper factor groups, or, equivalently, any of its epimorphisms on itself is an isomorphism, i.e., an automorphism. This property was first proved by the Swiss mathematician H.
Kaigorodov, Evgeniy Vladimirovich
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VNR rings, $\Pi$-regular rings and annihilators [PDF]
, 1974 summary:Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered.
Yue Chi Ming, Roger +3 more
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On the mapping xy→(xy)n in an associative ring
International Journal of Mathematics and Mathematical Sciences, 2004 We consider the following condition (*) on an associative ring R:(*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy)=(xy)n(x,y) for some positive integer n(x,y)>1. Commutativity and
Scott J. Beslin, Awad Iskander
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Noetherian and Artinian ordered groupoids—semigroups
International Journal of Mathematics and Mathematical Sciences, 2005 Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959.
Niovi Kehayopulu, Michael Tsingelis
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SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS [PDF]
, 2017 The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical,
Velasco, Ulyses
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Covering theorems for Artinian rings [PDF]
, 1997 The covering properties of Artinian rings which depend on their additive structure only, are ...
Bódi, Viktor +3 more
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Subrings of I-rings and S-rings
International Journal of Mathematics and Mathematical Sciences, 1997 Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
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Trivial Extension of π-Regular Rings [PDF]
Engineering and Technology Journal, 2016 In this paper we investigate if it is possible that the trivial extension ring T(R,R) inherit the properties of the ring R and present the relationship between the trivial extension T(R,M) of a ring R by an R-module M and theπ-regularity of Rby taking ...
Areej M. Abduldaim
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Topologically left artinian rings
Journal of Algebra, 1985 In this paper are considered linearly topologized rings with identity all whose factor-modules at open left ideals are artinian (TA-rings). In the characterization of TA-rings an important role is played by a minimal cogenerator \({}_ RV\) of the class of \(R\)-torsion left \(R\)-modules. Some results about structure and features of the module \({}_ RV\
MENINI, Claudia, A. ORSATTI
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