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On modules that complement direct summands
On modules that complement direct summandsopenaire +1 more source
Matrix Rings with Summand Intersection Property [PDF]
Czechoslovak Mathematical Journal, 2003 summary:A ring $R$ has right SIP (SSP) if the intersection (sum) of two direct summands of $R$ is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property.
Tercan, A. +3 more
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Submodules and direct summands
Journal of Mathematical Sciences, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abyzov, A. N., Tuganbaev, A. A.
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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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Generalized direct summands in an Abelian category
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1985An Abelian group \(A\) is quasi-splitting if there is an integer \(n\) and a subgroup \(C\) such that \(nA\leq tA\oplus C\leq A\) where \(tA\) is the torsion subgroup of \(A\). \textit{C. P. Walker} [Acta. Math. Acad. Sci. Hung. 15, 157-160 (1964; Zbl 0136.290)] proved that \(A\) is quasi-splitting if and only if \(tA\rightarrowtail A\twoheadrightarrow
T.H., Fay, M.J., Schoeman
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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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