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Modules in Which Sums or Intersections of Two Direct Summands Are Direct Summands
Journal of Mathematical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abyzov A., Tuganbaev A.
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Archiv der Mathematik, 2002
Let \(R\) be a ring. All modules considered are right modules. A module \(M\) is said to be (finitely) product-rigid if any (finitely presented) direct summand of a product of copies of \(M\) having a local endomorphism ring is isomorphic to some indecomposable direct summand of \(M\) itself.
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Let \(R\) be a ring. All modules considered are right modules. A module \(M\) is said to be (finitely) product-rigid if any (finitely presented) direct summand of a product of copies of \(M\) having a local endomorphism ring is isomorphic to some indecomposable direct summand of \(M\) itself.
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Direct Summands of ⊕-Supplemented Modules
Algebra Colloquium, 2007A module M is called ⊕-supplemented if every submodule of M has a supplement that is a direct summand of M. It is shown that if M is a ⊕-supplemented module and r(M) is a coclosed submodule of M for a left preradical r, then r(M) is a direct summand of M, and both r(M) and M/r(M) are ⊕-supplemented.
Nil Orhan +2 more
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Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978
SynopsisWe discuss convexl-subgroups of anl-groupGin their role as direct summands, not so much ofGas of each other. This is done by writingA≥dBfor subgroupsA, Bto mean thatAis a direct summand ofB, and studying the properties of the resulting poset. It is shown to be a hypolattice, that is, to have local lattice properties in a certain sense.
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SynopsisWe discuss convexl-subgroups of anl-groupGin their role as direct summands, not so much ofGas of each other. This is done by writingA≥dBfor subgroupsA, Bto mean thatAis a direct summand ofB, and studying the properties of the resulting poset. It is shown to be a hypolattice, that is, to have local lattice properties in a certain sense.
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Direct summands of vector groups
Acta Mathematica Hungarica, 1990Cartesian products of subgroups of the rationals are called vector groups. The author deals with the well-known problem whether the class of vector groups is closed under taking direct summands. The answer is yes in some special cases considered in recent years. The author provides a Lemma 2 (p. 207) which serves for the purpose to overcome a defective
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Rings with many direct summands
Archiv der Mathematik, 1991Let R be a ring, and let X be a class of right R-modules which contains the zero module, is closed under isomorphism, and is such that every module in X has finite uniform dimension. The author investigates the situation in which every cyclic right R-module is the direct sum of a projective module and a module in the class X. A characterisation of such
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Modules with many direct summands
Journal of Mathematical Sciences, 2008We study rings over which all right modules are I0-modules. All rings are assumed to be associative and with nonzero identity element. For a module M , a submodule N of M is said to be superfluous if N +P = M for every proper submodule P of the module M .
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Isomorphic minimal direct summands of QTAG-modules
São Paulo Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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MODULES WHOSE DIRECT SUMMANDS ARE FI-EXTENDING
2017WOS ...
TaşdEmir, Oktay, Karabacak, F.
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