Anh, Pham Ngoc and Siddoway, M.F. (2016) Divisibility Theory of Arithmetical Rings with One Minimal Prime Ideal. COMMUNICATIONS IN ALGEBRA, 44 (2). pp. 823836. ISSN 00927872
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Abstract
Continuing the study of divisibility theory of arithmetical rings started in [1] and [2], we show that the divisibility theory of arithmetical rings with one minimal prime ideal is axiomatizable as Bezout monoids with one minimal mprime filter. In particular, every Bezout monoid with one minimal mprime filter is orderisomorphic to the partially ordered monoid with respect to inverse inclusion, of principal ideals in a Bezout ring with a smallest prime ideal. Although this result can be considered as a satisfactory answer to the divisibility theory of both semihereditary domains and valuation rings, the general representation theory of Bezout monoids is still open. © 2016, Copyright © Taylor & Francis Group, LLC.
Item Type:  Article 

Uncontrolled Keywords:  SPECTRUM; mPrime filter; Bezout rings 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  03 Jan 2017 18:22 
Last Modified:  09 Jan 2017 08:34 
URI:  http://real.mtak.hu/id/eprint/44385 
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