(Generalized) filter properties of the amalgamated algebra

Yusof Azimi

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 3, page 133-140
  • ISSN: 0044-8753

Abstract

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Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ⋈ f J : = { ( a , f ( a ) + j ) ∣ a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ⋈ f J is a (generalized) filter ring.

How to cite

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Azimi, Yusof. "(Generalized) filter properties of the amalgamated algebra." Archivum Mathematicum 058.3 (2022): 133-140. <http://eudml.org/doc/298398>.

@article{Azimi2022,
abstract = {Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ and $j\in J\rbrace $ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we determine when $R\bowtie ^fJ$ is a (generalized) filter ring.},
author = {Azimi, Yusof},
journal = {Archivum Mathematicum},
keywords = {amalgamated algebra; Cohen-Macaulay ring; $f$-ring; generalized $f$-ring},
language = {eng},
number = {3},
pages = {133-140},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {(Generalized) filter properties of the amalgamated algebra},
url = {http://eudml.org/doc/298398},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Azimi, Yusof
TI - (Generalized) filter properties of the amalgamated algebra
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 133
EP - 140
AB - Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ and $j\in J\rbrace $ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we determine when $R\bowtie ^fJ$ is a (generalized) filter ring.
LA - eng
KW - amalgamated algebra; Cohen-Macaulay ring; $f$-ring; generalized $f$-ring
UR - http://eudml.org/doc/298398
ER -

References

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