Center-like subsets in prime rings with derivations and endomorphisms
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DOI: 10.1007/s00010-021-00789-8
Abstract: Let R be a prime ring. In this paper it’s proved that certain subsets of R defined by conditions involving derivations and endomorphisms coincide with the center of R. In fact, our results generalize and… read more here.
Keywords: prime rings; subsets prime; derivations endomorphisms; rings derivations ... See more keywords
On prime rings whose central closure is finitely generated
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DOI: 10.1016/j.jalgebra.2017.06.021
Abstract: Abstract The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the… read more here.
Keywords: prime rings; closure; finitely generated; whose central ... See more keywords
Generalized derivations with multilinear polynomials in prime rings
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DOI: 10.1080/00927872.2018.1468899
Abstract: Abstract Let R be a prime ring of characteristic different from two with Utumi quotient ring U and extended centroid C, be a multilinear polynomial over C, which is not central valued on R. Suppose… read more here.
Keywords: prime rings; multilinear polynomials; polynomials prime; derivations multilinear ... See more keywords
On Lie Ideals and Automorphisms in Prime Rings
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DOI: 10.1134/s0001434620010137
Abstract: Let R be a prime ring of characteristic different from 2 with center Z and extended centroid C , and let L be a Lie ideal of R . Consider two nontrivial automorphisms α and… read more here.
Keywords: ideals automorphisms; lie ideals; prime rings; automorphisms prime ... See more keywords
Special Mappings with Central Values on Prime Rings
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DOI: 10.1142/s1005386720000334
Abstract: In this paper we investigate commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy certain algebraic identities. Furthermore, we provide examples to show ... read more here.
Keywords: values prime; mappings central; prime rings; central values ... See more keywords
Engel type identities with generalized derivations in prime rings
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DOI: 10.1142/s1793557118500559
Abstract: Let R be a noncommutative prime ring with its Utumi ring of quotients U, C = Z(U) the extended centroid of R, G a generalized derivation of R and I a nonzero ideal of R.… read more here.
Keywords: derivations prime; prime rings; type identities; identities generalized ... See more keywords