Properties of K-Isomorphism on K-Algebra

Lestari, Fanny Dwi; Hafiyusholeh, Mohammad; Asyhar, Ahmad Hanif; Utami, Wika Dianita; Arifin, Ahmad Zaenal

doi:10.1088/1742-6596/1211/1/012053

Cited by 2 publications

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“…As for the formation of the p-poor module, it was found that an R-module, which is the result of the direct sum of all cyclic modules over R is a p-poor module [2]. This paper is inspired by similar ideas and problems in [4] [5], where there is a lemma introduced by Stephen Schanuel in 1958 and known as the Schanuel's lemma in projective modules. That lemma associated with the equivalence of two modules K1 and K2 provided that there are two projective modules P1 and P2 such that 1 ⊕ 2 is isomorphic to 2 ⊕ 1 .…”

Section: Introductionmentioning

confidence: 97%

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Schanuel's Lemma in P-Poor Modules

Maulana

2019

JMM

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Modules are a generalization of the vector spaces of linear algebra in which the “scalars” are allowed to be from a ring with identity, rather than a field. In module theory there is a concept about projective module, i.e. a module over ring R in which it is projective module relative to all modules over ring R. Next, there is the fact that every module over ring R is projective module relative to all semisimple modules over ring R. If P is a module over ring R which it’s projective relative only to all semisimple modules over ring R, then P is called p-poor module. In the discussion of the projective module, there is a lemma associated with the equivalence of two modules K1 and K2 provided that there are two projective modules P1 and P2 such that is isomorphic to . That lemma is known as Schanuel’s lemma in projective modules. Because the p-poor module is a special case of the projective module, then in this paper will be discussed about Schanuel’s lemma in p-poor modules

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Section: Introductionmentioning

confidence: 97%

“…modules over a ring R. In this paper, Mod-R denotes the set of all right R-modules and SSMod-R the set of all semisimple right R-modules. An R-module is called a semisimple module if that module is a direct sum of simple modules [5]. A non-zero R-module is called a simple module if that module has no non-trivial submodules.…”

Section: Introductionmentioning

confidence: 99%