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Rings whose finitely generated right ideals are quasi-projective
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Askar A. Tuganbaev
Published/Copyright:
August 7, 2015
Abstract
An invariant ring A is arithmetical if and only if every finitely generated ideal M of the ring A is a quasi-projective A-module and every endomorphism of this module may be extended to an endomorphism of the module AA. An invariant semiprime ring A is arithmetical if and only if every finitely generated ideal M of the ring A is a quasi-projective A-module.
Keywords: arithmetical ring; quasi-projective module; skew-projective module; integrally closed module; distributive module
Received: 2014-11-13
Published Online: 2015-8-7
Published in Print: 2015-8-1
© 2015 by Walter de Gruyter Berlin/Boston
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- Frontmatter
- On groups with automorphisms generating recurrent sequences of the maximal period
- Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
- Free commutative medial n-ary groupoids
- Complexity of implementation of parity functions in the implication–negation basis
- Closed classed of three-valued logic that contain essentially multiplace functions
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Keywords for this article
arithmetical ring;
quasi-projective module;
skew-projective module;
integrally closed module;
distributive module
Articles in the same Issue
- Frontmatter
- On groups with automorphisms generating recurrent sequences of the maximal period
- Classification of correlation-immune and minimal correlation-immune Boolean functions of 4 and 5 variables
- Free commutative medial n-ary groupoids
- Complexity of implementation of parity functions in the implication–negation basis
- Closed classed of three-valued logic that contain essentially multiplace functions
- A generalization of Ore’s theorem on irreducible polynomials over a finite field
- Rings whose finitely generated right ideals are quasi-projective
