Residual smallness in commutative algebra

Adam Salminen

Residual smallness in commutative algebra

Kettering University

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

Abstract

<div class="line" id="line-7"> In Oman and Salminen [ <a href="https://www.tandfonline.com/doi/abs/10.1080/00927872.2017.1376213?journalCode=lagb20#"> 19 </a> ], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring  R  with identity is residually smallif for every  r ∈ R &ssetmn;{0}, there exists an ideal  I r  of  R  such that  r ∉ I r  and | R ∕ I r |<| R |. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. </div>

Original language	American English
Journal	Communications in Algebra
Volume	46
State	Published - Oct 30 2017

Disciplines

Mathematics
Algebra

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Cite this

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title = "Residual smallness in commutative algebra",

abstract = " In Oman and Salminen [ 19 ], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring  R  with identity is residually smallif for every  r ∈ R &ssetmn;{0}, there exists an ideal  I r  of  R  such that  r ∉ I r  and | R ∕ I r |<| R |. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. ",

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AB - In Oman and Salminen [ 19 ], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring  R  with identity is residually smallif for every  r ∈ R &ssetmn;{0}, there exists an ideal  I r  of  R  such that  r ∉ I r  and | R ∕ I r |<| R |. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules.

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JO - Communications in Algebra

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