Projectives in a class of lattice ordered modules

Powell, Wayne B.

doi:10.1007/bf02483820

Cited by 9 publications

(3 citation statements)

References 8 publications

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“…However, to date the only result in this direction is found in Powell [15] where it is shown that the free algebras of rank greater than one in a rather large class of /-modules have no nontrivial cardinal summands.…”

Section: Henceforth We Let G/ = 4>(g¡) = ^(G)mentioning

confidence: 99%

Free products of abelian 𝑙-groups are cardinally indecomposable

Powell¹,

Tsinakis²

1982

Proc. Amer. Math. Soc.

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Section: Henceforth We Let G/ = 4>(g¡) = ^(G)mentioning

confidence: 99%

Free products of abelian 𝑙-groups are cardinally indecomposable

Powell¹,

Tsinakis²

1982

Proc. Amer. Math. Soc.

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“…However, to date the only result in this direction is found in Powell [15] where it is shown that the free algebras of rank greater than one in a rather large class of f-modules have no nontrivial cardinal summands. However, to date the only result in this direction is found in Powell [15] where it is shown that the free algebras of rank greater than one in a rather large class of f-modules have no nontrivial cardinal summands.…”

Section: Theorem 6 No Vector Lattice Is Decomposable Nontrivially Bomentioning

confidence: 99%

Free Products of Abelian l-Groups are Cardinally Indecomposable

Powell¹,

Tsinakis²

1982

Proceedings of the American Mathematical Society

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 138.253.100.121 on Fri, ABSTRACT. We show that a well-known theorem of Baer and Levi concerning the impossibility of simultaneous decomposition of a group into a free product and a direct sum has an analogue for abelian lattice ordered groups. Specifically we prove that an abelian lattice ordered group cannot be decomposed both into a free product and into a cardinal sum.

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“…Background on lattice ordered groups and modules in general can be found in Bigard, Keimel and Wolfenstein [2]. The only paper to date investigating free products of fmodules is Cherri and Powell [3], although several papers on free f-modules help introduce the subject (see Bigard [1], Powell [10], or Powell and Tsinakis [14]). …”

Section: Introductionmentioning

confidence: 99%