REAL

Generalization of a Theorem of Clifford

Pham Ngoc, Anh (2016) Generalization of a Theorem of Clifford. ACTA MATHEMATICA VIETNAMICA, 41 (3). pp. 471-480. ISSN 0251-4184

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Abstract

We prove that the multiplicative monoid of principal ideals partially ordered by reverse inclusion, called the divisibility theory, of a Bezout ring R with one minimal prime ideal is a factor of the positive cone of a lattice-ordered abelian group by an appropriate filter if the localization of R at its minimal prime ideal is not a field. This result extends a classical result of Clifford (Am. J. Math. 76:631–646, 1954) saying that the divisibility theory of a valuation ring is a Rees factor of the positive cone of a totally ordered abelian group and suggests to modify Kaplansky’s (later disproved) conjecture (Fuchs and Salce, Mathematical Surveys and Monographs 84, 2001) as to whether a Bezout ring whose localization at every minimal prime ideal has at least three ideals is the factor of an appropriate Bezout domain. © 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

Item Type: Article
Uncontrolled Keywords: SPECTRUM; Prime filter; Lattice-ordered abelian group; Bezout monoid
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 03 Jan 2017 07:35
Last Modified: 03 Jan 2017 07:35
URI: http://real.mtak.hu/id/eprint/44223

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