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

Abstract

AbstractIn 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 {\mathrm{SK}_{0}}-groups. Consequently, we get that there is a one-one correspondence between isomorphism classes of ultramatricial algebras A whose {\mathrm{SK}_{0}(A)} is lattice-ordered over a given commutative chain semiring and isomorphism classes of countable MV-algebras.