ABOUT ONE MODIFICATION OF CONCEPTS OF COMPLETELY, REDUCIBILITY, periodicity and primarity FOR associative RINGs

2021 ◽  
Vol 26 (2) ◽  
pp. 12-22
Author(s):  
L. M. Martynov
Keyword(s):  
Associative Rings

Varieties satisfying semigroup identities: Algebras over a finite field and rings

2016 ◽  
Vol 26 (05) ◽  
pp. 985-1017
Author(s):  
Olga B. Finogenova
Keyword(s):  
Finite Field ◽  
Associative Algebras ◽  
Adjoint Semigroup ◽  
Semigroup Identities ◽  
Associative Rings

We study varieties of associative algebras over a finite field and varieties of associative rings satisfying semigroup or adjoint semigroup identities. We characterize these varieties in terms of “forbidden algebras” and discuss some corollaries of the characterizations.

scholarly journals A commutativity theorem for lefts-unital rings

1990 ◽  
Vol 13 (4) ◽  
pp. 769-774
Author(s):  
Hamza A. S. Abujabal
Keyword(s):  
Commutativity Theorem ◽  
Unital Ring ◽  
Commutativity Theorems ◽  
Associative Rings ◽  
Unital Rings

In this paper we generalize some well-known commutativity theorems for associative rings as follows: LetRbe a lefts-unital ring. If there exist nonnegative integersm>1,k≥0, andn≥0such that for anyx,yinR,[xky−xnym,x]=0, thenRis commutative.

scholarly journals On generalized derivations and commutativity of associative rings

2020 ◽  
Vol 40 (1) ◽  
pp. 49
Author(s):  
Bijan Davvaz ◽  
Deepak Kumar ◽  
Gurninder S. Sandhu
Keyword(s):  
Generalized Derivations ◽  
Associative Rings

scholarly journals A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings

2009 ◽  
Vol 52 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Jakob Cimprič
Keyword(s):  
Algebraic Geometry ◽  
Representation Theory ◽  
Representation Theorem ◽  
Commutative Rings ◽  
Real Algebraic Geometry ◽  
New Approach ◽  
Noncommutative Version ◽  
Quadratic Modules ◽  
Rings With Involution ◽  
Associative Rings

AbstractWe present a new approach to noncommutative real algebraic geometry based on the representation theory of C*-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand–Naimark representation theorem for commutative C*-algebras. A noncommutative version of Gelfand–Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution.

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