IJPAM: Volume 115, No. 2 (2017)

Title

ON AN EXTENSION OF SHARP DOMAINS

Authors

Chahn Yong Jung$^1$, Waseem Khalid$^2$, Waqas Nazeer$^3$,
Tayyab Tariq$^4$, Shin Min Kang$^5$
$^1$Department of Business Administration
Gyeongsang National University
Jinju, 52828, KOREA
$^{2,4}$Department of Mathematics
The University of Lahore
Pakpattan, 57400, PAKISTAN
$^3$Division of Science and Technology
University of Education
Lahore, 54000, PAKISTAN
$^5$Department of Mathematics and RINS
Gyeongsang National University
Jinju 52828, KOREA

Abstract

As an extension of the class of sharp domains introduced by Ahmad et al., we introduce and study a class of integral domains $D$ characterized by the property that whenever $X,Y_{1},Y_{2}$ are nonzero ideals of $D$ with ${X \supseteq Y_{1}Y_{2}}$, there exist nonzero ideals $Z_{1}$ and $Z_{2}$ such that $X_{w}$ = $(Z_{1}Z_{2})_{w}$, $(Z_{1})_{w} \supseteq Y_{1}$ and $(Z_{2})_{w} \supseteq Y_{2}$. We call $D$ with this property a $w$-sharp domain. We show that every fraction ring of a $w$-sharp domain is $w$-sharp, that a $w$-Dedekind domain is $w$-sharp and that every nonzero finitely generated ideal of a $w$-sharp domain is $w$-invertible.

History

Received: January 31, 2017
Revised: July 5, 2017
Published: July 14, 2017

AMS Classification, Key Words

AMS Subject Classification: 13A15, 13F05
Key Words and Phrases: Schreier domain, pseudo-Dedekind domain, Prüfer domain

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How to Cite?

DOI: 10.12732/ijpam.v115i2.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 2
Pages: 353 - 360


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