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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Ultramatricial algebras over commutative chain semirings and application to MV-algebras

Antonio Di Nola / Giacomo Lenzi / Tran Giang Nam
Published Online: 2019-10-27 | DOI: https://doi.org/10.1515/forum-2019-0056

Abstract

In this paper, we give a complete description of strongly projective semimodules over a semiring which is a finite direct product of matrix semirings over commutative chain semirings. We then classify ultramatricial algebras over commutative chain semirings by their ordered SK0-groups. Consequently, we get that there is a one-one correspondence between isomorphism classes of ultramatricial algebras A whose SK0(A) is lattice-ordered over a given commutative chain semiring and isomorphism classes of countable MV-algebras.

Keywords: Strongly projective semimodule; ultramatricial algebras over semirings; MV-algebras

MSC 2010: 16Y60; 06D35; 16E20; 18G05

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About the article


Received: 2019-02-27

Revised: 2019-09-20

Published Online: 2019-10-27


The third author is partially supported by Vietnam Ministry of Education and Training under the grant number B2018.SPD.02.


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2019-0056.

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