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Direct summands inl-groups [PDF]
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.
John Boris Miller
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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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Isomorphic minimal direct summands of QTAG-modules
Sao Paulo Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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 direct products of Abelian groups
Archiv Der Mathematik, 1960Elbert A Walker, Walker Elbert A
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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.
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