Results 201 to 210 of about 2,272 (232)

On Rings with Many Endomorphisms

Canadian Mathematical Bulletin, 1976
AbstractAll rings have an identity, all homomorphisms map identities to identities, all homomorphisms on algebras over fields are algebra homomorphisms. A ring R is a quotient-embeddable ring (a QE-ring) if for any proper ideal a of R there is an endomorphism of R whose kernel is the ideal a.
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On the Endomorphisms of a Polynomial Ring

Canadian Journal of Mathematics, 1976
This paper arises in the attempt to solve the following problem related to the Zariski Problem. Let A be a polynomial ring in three variables over a field, . Suppose there is a subring B of A such that k ⊆ B and there is variable t over B such that B[t] = A. Then is it true that B is a polynomial ring over k?
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On Commuting Rings Of Endomorphisms

Canadian Journal of Mathematics, 1956
Various problems concerning the general theory of centralizers of modules which are not assumed to be completely reducible have been discussed by Fitting (3), Brauer (2), and Nakayama. In this paper we present a new approach to some of these questions, which has its origin in Weyl's discussion (15) of the centralizer of a finite group of collineations.
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Endomorphism Rings of Abelian Groups

Journal of Mathematical Sciences, 2002
The authors have compiled, under nine chapter headings, a comprehensive review of the literature on endomorphism rings of Abelian groups. They target an audience of specialists in Abelian group theory, as will this review. The authors state that their purpose is to ``try to give an idea of the possibilities, methods of proofs, and relations between ...
Krylov, P. A., Mikhalev, A. V., Tuganbaev, A. A.   +2 more
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Ring Properties of Endomorphism Rings

2003
In Chapter 3 the following topics are considered: the finite topology (Section 14); endomorphism rings with the minimum condition (Section 15); Hom(A, B) as a Noetherian module over End(B) (Section 16); mixed groups with Noetherian endomorphism rings (Section 17); regular endomorphism rings (Section 18); commutative and ...
Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev   +2 more
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Endomorphism rings of Abelian groups as isomorphic restrictions of full endomorphism rings. II

Acta Mathematica Hungarica, 1992
[For part I cf. Period Math. Hung. 24, 129-133 (1992).] A group is called cotorsion-free if it is reduced, torsion-free and contains no subgroups which are isomorphic to the additive group of the ring of \(p\)-adic integers for some prime \(p\neq 1\). A ring is cotorsion- free it its additive group is cotorsion-free. \textit{M.
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Endomorphism Semigroups of Sums of Rings

Canadian Mathematical Bulletin, 1974
Let R= 〈R, +, •〉 be the cartesian sum of the rings Ri, i= 1, 2,…, n denoted by , and recall that R is a ring under the componentwise operations. It is well-known (e.g. [1], p. 212) that the endomorphisms of the group 〈R, + 〉 form a ring HomZR (under function addition and composition) and moreover HomZR is isomorphic to the matrix ring under the usual ...
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Endomorphism rings of abelian groups

Algebra and Logic, 1988
Let k be a non-countable regular non-weakly compact cardinal.
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Modules over Endomorphism Rings

Mathematical Notes, 2004
All rings are assumed to be associative and to have non-zero identity. A module is called a Bezout module if all its finitely generated submodules are cyclic, and is called distributive if the lattice of its submodules is distributive. The main results established by the author are the following ones.
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Endomorphism Rings and Gabriel Topologies

Canadian Journal of Mathematics, 1984
A basic tool in the usual presentation of the Morita theorems is the correspondence theorem for projective modules. Let RM be a left R-module and B = HomR(M, M). When M is a progenerator, there is a close connection (in fact a lattice isomorphism) between left R-submodules of M and left ideals of B, which can be applied to the solution of problems such
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