Results 101 to 110 of about 87,285 (205)
Two elementary commutativity theorems for generalized boolean rings
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper we prove that if R is a ring with 1 as an identity element in which xm−xn∈Z(R) for all x∈R and fixed relatively prime positive integers m and n, one of which is even, then R is commutative.
Vishnu Gupta
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Commutative Rings whose Matrix Rings are Baer Rings [PDF]
Proceedings of the American Mathematical Society, 1969 A ring R with unit element is a Baer ring if every left annihilator in R has the form Re, where e is an idempotent element. K. G. Wolfson has proven [3, Corollary 15], that if R is a Priifer ring (a commutative integral domain in which every finitely generated ideal is invertible) then the ring of endomorphisms of a finitely generated free module over ...
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S-J-Ideals: A Study in Commutative and Noncommutative Rings
Journal of MathematicsIn this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J-ideals apply to S-J-ideals and examine their ...
Alaa Abouhalaka +2 more
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Non-commutative Henselian rings
Journal of Algebra, 2009 7 pages; Added references, email and postal ...
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Effect of Polynomial Identity x[x, y] = (x[x, y])n in the Commutativity of Rings
Journal of Mathematical Extension, 2009 . In this paper we study some sufficient conditions for commutativity of a ring according to Jacobsons’idea. Jacobson proved that if R is a ring satisfying x n = x (n > 1) for each x ∈ R, then R is commutative.
Z. Tabatabaei
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Localization and Flatness in Quantale Theory
MathematicsThe study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales.
George Georgescu
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Finite Commutative Chain Rings
Finite Fields and Their Applications, 2001 A commutative ring with unit is called a chain ring if all its ideals form a chain under inclusion. All finite chain rings can be obtained in the following way: Let \(p\) be a prime, \(n,r>0\), \(f\in \mathbb{Z}_{p^n}[X]\) a monic polynomial, \(\deg(f)=r\) whose image in \(\mathbb{Z}_p[X]\) is irreducible and let \(\text{GR} (p^n,r): =\mathbb{Z}_{p^n ...
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Holographic Einstein rings of non-commutative black holes
European Physical Journal C: Particles and FieldsWith the help of AdS/CFT correspondence, we derive the desired response function of QFT on the boundary of the non-commutative black hole. Using the virtual optical system with a convex lens, we obtain the Einstein rings of the black hole from the ...
Xin-Yun Hu +3 more
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Projective Modules and Polynomials over the Hurwitz Quaternions
MathematicsA theorem of Sheshadri (Proc. Nat. Acad. Sci. USA 44 (1958) 456–458) shows that, when Λ is a commutative principal ideal domain, finitely generated projective modules over the polynomial ring Λ[t] are all free. The ring Γ of Hurwitz quaternions, that is,
Francis E. A. Johnson
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