Results 221 to 230 of about 28,026 (260)

On Symmetric Elements and Symmetric Units in Group Rings

Communications in Algebra, 2006
ABSTRACT Let R be a commutative ring, G a group, and RG its group ring. Let ϕ: RG → RG denote the R-linear extension of an involution ϕ defined on G. An element x in RG is said to be symmetric if ϕ (x) = x. A characterization is given of when the symmetric elements (RG)ϕ of RG form a ring. For many domains R it is also shown that (RG)ϕ is a ring if and
Jespers, Eric, Ruiz, M.
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On the Symmetric Hypercenter of a Ring

Canadian Journal of Mathematics, 1984
The hypercenter theorem [6] asserts that in a ring with no non-zero nil ideals an element commuting with a suitable power of each element of the ring must be central. In this paper we shall be concerned with a similar problem in the setting of rings with involution.
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*-Symmetric rings

Journal of Algebra and Its Applications
Let [Formula: see text] be a ∗-ring. Then [Formula: see text] is called a ∗-symmetric ring if for any [Formula: see text] implies [Formula: see text] Obviously, ∗-symmetric ring is certainly symmetric ring, while ∗-ring and symmetric ring does not equal ∗-symmetric ring.
Xinran Wang, Suting Fan, Junchao Wei
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A Note on Weakly Symmetric Rings

Canadian Mathematical Bulletin, 1974
T. Nakayama showed in [2, Theorem 13] that symmetric algebras have the property that the left and right annihilators of their two-sided ideals are equal. He also gave examples [2, p. 630] to show that QF algebras with this property are not necessarily symmetric, and that weakly symmetric algebras need not have this property.
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( g,e ) -Symmetric Rings

Algebra Colloquium
Let [Formula: see text] be a ring and [Formula: see text], [Formula: see text] in [Formula: see text], the set of idempotents of [Formula: see text]. Then [Formula: see text] is called [Formula: see text]-symmetric if [Formula: see text] implies [Formula: see text] for any [Formula: see text], [Formula: see text], [Formula: see text].
Meng, Fanyun, Wei, Junchao
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Generalized weakly symmetric rings

Journal of Pure and Applied Algebra, 2014
An associative ring \(R\) with identity is called generalized weakly symmetric (GWS) if for any \(a,b,c\in R\), \(abc=0\) implies that the element \(bac\) is nilpotent. Commutative rings, reduced rings and symmetric rings are all GWS. The author establishes several interesting results on GWS rings, such as: (1) a ring \(R\) is GWS if and only if the ...
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A symmetric generalization of $$\pi $$-regular rings

Ricerche di Matematica, 2021
In the paper under review, the author introduces the class of double regularly nil clean rings (or D-regularly nil clean rings for short): a unital, associative ring \(R\) is D-regularly nil clean if for each \(a\in R\) there exists an idempotent element \(e\in aRa\) such that \(a(1-e)\) is a nilpotent element (Definition 1.1).
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A question of passman on the symmetric ring of quotients

Israel Journal of Mathematics, 1989
The symmetric ring of quotients \(Q_ s(R)\) is an important subring of the Martindale ring of quotients of the prime ring R. It was introduced by V. K. Kharchenko in his work on Galois theory. It was known that \(Q_ s\) need not be a closure operator, but in the example given \(Q_ s\) was a closure operator on \(Q_ s(R)\).
Ara, Pere, Del Río, Angel
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Symmetric Units in Alternative Loop Rings

Algebra Colloquium, 2006
Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. For α = ∑ αℓℓ in a loop ring RL, define α♯= ∑ αℓℓ-1and call α symmetric if α♯= α. We find necessary and sufficient conditions under which the symmetric units are closed under multiplication (and hence form a subloop of the loop of ...
Goodaire, Edgar G., Polcino Milies, César   +1 more
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Symmetric Representation Rings are $λ$-Rings

2013
The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $λ$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the representation category, for any affine algebraic group scheme over a field of characteristic not two.
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