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Strongly regular near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1980 A strongly regular ring R is one in which for all x ∈ R, there is an a ∈ R with x = x2a. Equivalently, for all x there is an a with x = ax2. Such a ring is regular, duo, biregular, and a left and right V-ring. Moreover since R is reduced, all nilpotent elements are central (vacuously) and so all idempotent elements are central.
Gordon Mason
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Strongly Regular Extensions of Rings [PDF]
Nagoya Mathematical Journal, 1962 As defined by Arens and Kaplansky [2] a ring A is strongly regular (s.r.) in case to each a∊ A there corresponds x = xa ∊A depending on a such that a 2 x = a. In the present article a ring A is defined to be a s.r.
Carl Faith
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EXTENSIONS OF STRONGLY π-REGULAR RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2014 An ideal I of a ring R is strongly π-regular if for any x ∈ I there exist n ∈ N and y ∈ I such that x = xy. We prove that every strongly π-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any x ∈ I there exist two distinct m,n ∈ N such that x = x. Furthermore, we prove that an ideal I of a ring R is periodic if and only if
Huanyin Chen +2 more
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Strongly Semiunits and Tri-Regular Elements in Rings [PDF]
Eurasian Journal of Science and Engineering, 2018 In this paper we study semiunit elements in the group ring Z2G, where G is a cyclic group and we introduce and discuss strongly semiunit elements in Zn, for n=p, 2p, p2 where p is an odd prime.
Parween Ali Hummadi , Suham Hamad Awla
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Note on strongly regular near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1986 Let S be a semigroup. An element a of S is called right (resp. left) regular if a=a2x (resp. a=xa2) for some x∈S. If a is regular and right (resp. left) regular, a is called strongly right (resp. left) regular. As is well known, if a is strongly regular (i.e., right and left regular) then it is regular, more precisely, there exists uniquely an element ...
Motoshi Hongan
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Equimultiplicity Theory of Strongly F-Regular Rings [PDF]
Michigan Mathematical Journal, 2020 17 ...
Thomas Polstra, Ilya Smirnov
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A Generalization Of Regular And Strongly $Π$-regular Rings [PDF]
, 2019 We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical von Neumann regular rings and of the strongly $ $-regular rings. Some other close relationships with certain well-known classes of rings such as $ $-regular rings, exchange rings, clean rings ...
Peter Danchev
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On strongly regular near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1984 According to Mason [1] a right near-ring N is called (i) left (right) strongly regular if for every a there is an x in N such that a = xa2 (a = a2x) and (ii) left (right) regular if for every a there is an x in N such that a = xa2 (a = a2x) and a = axa.
Y. Venkateswara Reddy, C. V. L. N. Murty
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EP elements and *-strongly regular rings
Filomat, 2018 Let R be a ring with involution *. An element a 2 R is called *-strongly regular if there exists a projection p of R such that p ? comm2(a), ap = 0 and a + p is invertible, and R is said to be *-strongly regular if every element of R is *-strongly regular.
Hua Yao, Junchao Wei
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Weakly Semicommutative Rings and Strongly Regular Rings
Kyungpook mathematical journal, 2014 A ring R is called weakly semicommutative ring if for any a, b ∈ R∗ = R \ {0} with ab = 0, there exists n ≥ 1 such that either a = 0 and aRb = 0 or b = 0 and aRb = 0. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if
Long Wang, Junchao Wei
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