PMV-Algebras of Matrices

MV-algebras of various kinds have been heavily investigated in the recent times. The isomorphism theorems between the MV-algebras and the interval MV-algebras in the corresponding lattice-ordered algebraic structures support research that utilizes the established properties of these structures in order to obtain specific information about the initial MV-algebras. In this talk we will discuss a concrete shape of any product MV-algebra that naturally embeds in a real algebra of matrices. We will use the structure theorem about lattice-ordered real algebras of matrices. In particular we establish that PMValgebras in concern are precisely the intervals between the zero matrix and a conjugate of a certain positive matrix.