LATTICE DECOMPOSITION OF MODULES

J. M. GARCIA; P. JARA; L. M. MERINO

doi:https://doi.org/10.24330/ieja.969940

Makale detayları

LATTICE DECOMPOSITION OF MODULES

Yazarlar:

J. M. GARCIA | P. JARA | L. M. MERINO

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2021 Vol.30 Issue 30, pp.285-303

Belge Tipi:

Makale

Yayın Tarihi:

7/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000717826

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.969940

Özet:

 

The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module MMM produce these decompositions: the \emph{lattice decompositions}. In a first \textit{\'{e}tage} this can be done using endomorphisms of MMM, which produce a decomposition of the ring \EndR(M)\EndR(M)\End_R(M) as a product of rings, i.e., they are central idempotent endomorphisms. But since not every central idempotent endomorphism produces a lattice decomposition, the classical theory is not of application. In a second step we characterize when a particular module MMM has a lattice decomposition; this can be done, in the commutative case in a simple way using the support, \Supp(M)\Supp(M)\Supp(M), of MMM; but, in general, it is not so easy. Once we know when a module decomposes, we look for characterizing its decompositions. We show that a good framework for this study, and its generalizations, could be provided by the category σ[M]σ[M]\sigma[M], the smallest Grothendieck subcategory of \rModR\rModR\rMod{R} containing MMM.

Makale detayları

LATTICE DECOMPOSITION OF MODULES

Yazarlar: J. M. GARCIA | P. JARA | L. M. MERINO

Yayıncı: Abdullah HARMANCI

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Algebra 2021 Vol.30 Issue 30, pp.285-303

Belge Tipi: Makale

Yayın Tarihi: 7/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000717826

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.969940

Sayı

Yazarlar:

J. M. GARCIA | P. JARA | L. M. MERINO

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2021 Vol.30 Issue 30, pp.285-303

Belge Tipi:

Makale

Yayın Tarihi:

7/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000717826

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.969940