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.

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

Di Nola, A.;Lenzi, G.;
2020

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4728390
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