The smallest element of a lattice of ideals in semi-hereditary rings

Majid M. Ali

doi:10.1080/00927872.2021.1916823

The smallest element of a lattice of ideals in semi-hereditary rings

Majid M. Ali^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let R be a commutative ring with identity. A ring R is called a semi-hereditary ring if every finitely generated ideal in R is projective. For finitely generated ideals A and B in R, we consider the associated lattice of ideals in a semi-hereditary ring R (Formula presented.) In this note, we investigate the smallest element in (Formula presented.).

Original language	English
Pages (from-to)	4199-4207
Number of pages	9
Journal	Communications in Algebra
Volume	49
Issue number	10
DOIs	https://doi.org/10.1080/00927872.2021.1916823
Publication status	Published - 2021
Externally published	Yes

Keywords

Multiplication ideal
projective ideal
semi-hereditary ring

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2021.1916823

Cite this

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abstract = "Let R be a commutative ring with identity. A ring R is called a semi-hereditary ring if every finitely generated ideal in R is projective. For finitely generated ideals A and B in R, we consider the associated lattice of ideals in a semi-hereditary ring R (Formula presented.) In this note, we investigate the smallest element in (Formula presented.).",

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AB - Let R be a commutative ring with identity. A ring R is called a semi-hereditary ring if every finitely generated ideal in R is projective. For finitely generated ideals A and B in R, we consider the associated lattice of ideals in a semi-hereditary ring R (Formula presented.) In this note, we investigate the smallest element in (Formula presented.).

KW - Multiplication ideal

KW - projective ideal

KW - semi-hereditary ring

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The smallest element of a lattice of ideals in semi-hereditary rings

Abstract

Keywords

ASJC Scopus subject areas

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