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Dergiler / International Electronic Journal of Algebra / 2020 / Cilt: 27 - Sayı: 27

EM-HERMITE RINGS

Emad ABUOSBA
Manal GHANEM
Sayfa
88–101
Yayın Tarihi
2020-01-07
DOI
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We relate EM-Hermite rings to weakly semi-Steinitz rings, and characterize the case at which every finitely generated $R$-module with finite free resolution of length 1 is free.

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Amaç & Hipotez:A ring $R$ is called EM-Hermite if for each $a,b\in R$, there exist $% a_{1},b_{1},d\in R$ such that $a=a_{1}d,b=b_{1}d$ and the ideal $% (a_{1},b_{1})$ is regular.
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Temel Bulgular & Veri:We give several characterizations of EM-Hermite rings analogue to those for K-Hermite rings, for example, $R$ is an EM-Hermite ring if and only if any matrix in $M_{n,m}(R)$ can be written as a product of a lower triangular matrix and a regular $m\times m$ matrix.
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Sonuç & Katkı:We relate EM-Hermite rings to weakly semi-Steinitz rings, and characterize the case at which every finitely generated $R$-module with finite free resolution of length 1 is free.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hermite ring · K-Hermite ring · weakly semi-Steinitz ring

Abstract

A ring $R$ is called EM-Hermite if for each $a,b\in R$, there exist $% a_{1},b_{1},d\in R$ such that $a=a_{1}d,b=b_{1}d$ and the ideal $% (a_{1},b_{1})$ is regular. We give several characterizations of EM-Hermite rings analogue to those for K-Hermite rings, for example, $R$ is an EM-Hermite ring if and only if any matrix in $M_{n,m}(R)$ can be written as a product of a lower triangular matrix and a regular $m\times m$ matrix. We relate EM-Hermite rings to Armendariz rings, rings with a.c. condition, rings with property A, EM-rings, generalized morphic rings, and PP-rings. We show that for an EM-Hermite ring, the polynomial ring and localizations are also EM-Hermite rings, and show that any regular row can be extended to regular matrix. We relate EM-Hermite rings to weakly semi-Steinitz rings, and characterize the case at which every finitely generated $R$-module with finite free resolution of length 1 is free.

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Bu Makaleye Atıf Yap

ABUOSBA, E., GHANEM, M. (2020). EM-HERMITE RINGS. International Electronic Journal of Algebra, Cilt: 27 - Sayı: 27, 88–101. https://ajindex.com/articles/832269

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Kaynakça (12)

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