Results 181 to 190 of about 1,334 (223)

On PP-Endomorphism Rings [PDF]

Canadian Mathematical Bulletin, 1993
AbstractA characterization is given of when all kernels (respectively images) of endomorphisms of a module are direct summands, a necessary condition being that the endomorphism ring itself is a left (respectively right) PP-ring. This result generalizes theorems of Small, Lenzing and Colby-Rutter and shows that R is left hereditary if and only if the ...
W. K. Nicholson
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Commutative Endomorphism Rings [PDF]

Canadian Journal of Mathematics, 1971
The problem of classifying the torsion-free abelian groups with commutative endomorphism rings appears as Fuchs’ problems in [ 4 , Problems 46 and 47]. They are far from solved, and the obstacles to a solution appear formidable (see [ 4; 5 ]).
J. Zelmanowitz
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Abelian Groups With Sufficiently π-Regular Endomorphism Ring [PDF]

Russian Mathematics, 2018
The notion of π-regular endomorphism ring of an abelian group, which generalizes the notion of regular endomorphism ring, was introduced in papers of L. Fuchs and K. Rangaswamy.
V M Misyakov, Misyakov V M
exaly   +2 more sources

Local Morphisms and Modules with a Semilocal Endomorphism Ring [PDF]

Algebras and Representation Theory, 2006
We study local morphisms in the setting of general noncommutative rings. In particular, we apply local morphisms to study endomorphism rings of modules. We use our construction to determine classes of modules with semilocal endomorphism rings.
Alberto Facchini, Dolors Herbera, Facchini Alberto   +2 more
exaly   +2 more sources

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sp-Groups and Their Endomorphism Rings

Journal of Mathematical Sciences, 2021
A mixed abelian group \(G\) is called an \(sp\)-group if it can be embedded in a natural way in the direct product of its primary components. In the present paper, the authors provide a comprehensive study of these groups, with a special attention to the case of mixed groups of finite torsion-free rank.
Krylov, Petr Andreevich, Tuganbaev, Askar A., Tsarev, A. V.   +2 more
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COUNTABLE RINGS AS ENDOMORPHISM RINGS

The Quarterly Journal of Mathematics, 1988
Let \(\sum \leq \prod\) be the direct sum and product of countably many copies of the integers, let \(\sum \leq D\leq \prod\) such that D/\(\sum\) is the divisible part of \(\prod /\sum\), and let \(e_ n=(\delta_{in})_{i\in {\mathbb{N}}}\in \prod\) be the generalized n-th unit vector.
Dugas, M., Irwin, J., Khabbaz, S.
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Endomorphism rings of bimodules

Periodica Mathematica Hungarica, 2014
For an integral domain \(R\), the endomorphism ring of a torsion-free \(R\)-module is torsion-free, as well. The authors investigate if this remains true for non-commutative rings, where ``torsion-free'' is replaced by ``non-singular''. Let \(R\) be a unital but not necessarily commutative ring. A right module \(M\) over \(R\) is right non-singular if \
Albrecht, Ulrich F., Göbel, Rüdiger
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Clean endomorphism rings

Archiv der Mathematik, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholson, W. K., Varadarajan, K., Zhou, Y.   +2 more
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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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