Construction of core regular double MS-algebras

Abstract

In this paper, we introduce and characterize core regular double MS-algebras.
A construction of a core regular double MS-algebra M[2] via a de Morgan algebra
M is given. A one to one correspondence between the class of de Morgan algebras
and the class of core regular double MS-algebras is obtained. According to such
construction we investigate many properties of core regular double MS-algebras
deal with subalgebras, homomorphisms, atoms and dual atoms. A description of
atomic core regular double MS-algebras is established. Also, we discuss some
properties of complete core regular double MS-algebras.