Schanuel's Lemma in P-Poor Modules

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...

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Autor principal:	Iqbal Maulana
Formato:	article
Lenguaje:	EN
Publicado:	Department of Mathematics, UIN Sunan Ampel Surabaya 2019
Materias:	projective module, semisimple module, p-poor module, schanuel’s lemma Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4f71c16201ea4830a708d76c3027202f
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id	oai:doaj.org-article:4f71c16201ea4830a708d76c3027202f
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spelling	oai:doaj.org-article:4f71c16201ea4830a708d76c3027202f2021-12-02T13:45:44ZSchanuel's Lemma in P-Poor Modules2527-31592527-316710.15642/mantik.2019.5.2.76-82https://doaj.org/article/4f71c16201ea4830a708d76c3027202f2019-10-01T00:00:00Zhttp://jurnalsaintek.uinsby.ac.id/index.php/mantik/article/view/655https://doaj.org/toc/2527-3159https://doaj.org/toc/2527-3167Modules 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 modulesIqbal MaulanaDepartment of Mathematics, UIN Sunan Ampel Surabayaarticleprojective module, semisimple module, p-poor module, schanuel’s lemmaMathematicsQA1-939ENMantik: Jurnal Matematika, Vol 5, Iss 2, Pp 76-82 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	projective module, semisimple module, p-poor module, schanuel’s lemma Mathematics QA1-939
spellingShingle	projective module, semisimple module, p-poor module, schanuel’s lemma Mathematics QA1-939 Iqbal Maulana Schanuel's Lemma in P-Poor Modules
description	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
format	article
author	Iqbal Maulana
author_facet	Iqbal Maulana
author_sort	Iqbal Maulana
title	Schanuel's Lemma in P-Poor Modules
title_short	Schanuel's Lemma in P-Poor Modules
title_full	Schanuel's Lemma in P-Poor Modules
title_fullStr	Schanuel's Lemma in P-Poor Modules
title_full_unstemmed	Schanuel's Lemma in P-Poor Modules
title_sort	schanuel's lemma in p-poor modules
publisher	Department of Mathematics, UIN Sunan Ampel Surabaya
publishDate	2019
url	https://doaj.org/article/4f71c16201ea4830a708d76c3027202f
work_keys_str_mv	AT iqbalmaulana schanuelslemmainppoormodules
_version_	1718392495487844352

Schanuel's Lemma in P-Poor Modules

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