Results 41 to 50 of about 1,198,003 (194)
Classical quotient rings of generalized matrix rings
International Journal of Mathematics and Mathematical Sciences, 1995 An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a finite set of orthogonal idempotents of R whose sum is 1.
David G. Poole, Patrick N. Stewart
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Proceedings of the American Mathematical Society, 1973 The main results proved in this paper are that if R R is a semiprime ring satisfying a polynomial identity then (1) the maximal right quotient ring of R R is also P.I. and (2) every essential one-sided ideal of R R contains an essential two-sided ideal of R R .
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Remarks on derivations on semiprime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy + d(xy) = yx + d(yx) for all x, y in R, or (ii) xy − d(xy) = yx − d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.
Mohamad Nagy Daif, Howard E. Bell
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Embeddings of semiprime rings into semisimple Artinian rings [PDF]
arXiv, 2023 Goldie's Theorem implies that a semiprime left Goldie ring is embeddable into a semisimple Artinian ring. On the other hand, there are domains that are not embeddable into division rings. A criterion for a semiprime ring being embeddable into a semisimple Artinian ring is given.
arxiv
On S-Prime and S-Semiprime RΓ-Submodules of RΓ-Module
, 2021 Let R be a Γ-ring and G be a RΓ-module. Aproper RΓ-submodule E of G is said to be S-prime (S-semiprime) RΓ-submodule of G whenever μ(K) ⊆ E ( μ(m) γ μ(m) E ), for some K be a RΓ-submodule of G, where End (G), y Γ and m G, then K ⊆ E or M(G)⊆ E ( μ(m) E).
Ali Abd Alhussein Zyarah, N. Al-Mothafar
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Commutativity results for semiprime rings with derivations
International Journal of Mathematics and Mathematical Sciences, 1998 We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x),d(y)]=0 for all x,y∈R, to the case of semiprime rings. An extension of this result is proved for a two-sided ideal but is shown to be not true for a one-sided ...
Mohammad Nagy Daif
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Symmetry, 2022 The nature of universe problems is ambiguous due to the presence of asymmetric data in almost all disciplines, including engineering, mathematics, medical sciences, physics, computer science, operations research, artificial intelligence, and management ...
K. Porselvi +3 more
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Semiprime SF-rings whose essential left ideals are two-sided
International Journal of Mathematics and Mathematical Sciences, 1994 It is proved that if R is a semiprime ELT-ring and every simple right R-module is flat then R is regular. Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question.
Zhang Jule, Du Xhianneng
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, 2015 Let M be a semiprime -ring with involution satisfying the con- dition that abc = abc (a, b, c ∈ M and , ∈ ). An additive mapping d : M → M is called -derivation if d(xy) = d(x) y +xd(y).
A. K. Kadhim, Hajar Sulaiman, A. Majeed
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S-Semiprime Submodules and S-Reduced Modules
Journal of Mathematics, 2020 This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity.
Ayten Pekin +2 more
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