Idealization of EM-Hermite rings
Commun. Korean Math. Soc.
Published online August 27, 2019
Hiba Abdelkarim, Emad Abuosba, and Manal Ghanem
The University of Jordan
Abstract : A commutative ring with unity R is called EM-Hermite if for each a,b∈R there exist c,d,f∈R such that a=cd,b=cf and the ideal (d,f) is regular in R. We showed in this article that R is a PP-ring if and only if the idealization R(+)R is an EM-Hermite ring if and only if R[x]/(xⁿ⁺¹) is an EM-Hermite ring for each n∈ℕ.
We generalise some results, and answer some questions in the literature.
Keywords : EM-Hermite ring, PP-ring, Idealization
MSC numbers : 13A, 13B25, 13B30, 13C10
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd