Commutator constraints - Open Access .click

Rendiconti del Circolo Matematico di Palermo Series 2, 2022
In this paper, the authors study the mappings satisfying some algebraic identities with endomorphisms (epimorphisms) acting on prime ideals and study there connection with commutativity of a quotient ring \(R/P\). Some known results are generalized.
Oukhtite, Lahcen, Bouchannafa, Karim
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Commutativity Theorems for Rings with Constraints Involving a Commutative Subset

Results in Mathematics, 1987
Let R denote a ring. Let A be a commutative subset containing all elements of R with square 0; let E be the set of idempotents of R; let \(q>1\) be an integer. The first theorem asserts that R must be commutative if it has the following two properties: (i) if x,y\(\in R\) and x-y\(\in A\), then \(x^ q=y^ q\) or x and y both centralize A; (ii) \(R ...
Tominaga, Hisao, Yaqub, Adil
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Commutativity theorems for s-unital rings with constraints on commutators

Results in Mathematics, 1992
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Abujabal, Hamza A. S., Perić, Veselin
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Commutativity of Rings with Constraints on Commutators, II

Results in Mathematics, 2000
[For part I see ibid. 5, 123-131 (1985; Zbl 0606.16023).] The author proves commutativity of an associative ring \(R\) satisfying one of the following conditions: (1) for each \(x,y\in R\) there exists a co-monic polynomial \(p(t)\in tZ[t]\), such that \([x,y]=[x,y](p(xy)-p(yx))\); (2) for each \(x,y\in R\) there exist \(p(t),q(t)\in tZ[t]\) with \(q(t)
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commutativity theorems
commutativity
nilpotent elements

mathematics
rings with polynomial identity
fos: physical sciences

fos: computer and information sciences
polynomial identities
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