Abstract
In this paper, we introduce the concepts of Stone elements, central elements and Birkhoof central elements of a double MS-algebra and study their related properties. We observe that the center C(L) of a double MS -algebra L is precisely the Birkhoof center BC(L) of L. A complete description of factor congruences on a double MS-algebra is given by means of the central elements. A characterization of balanced factor congruences of double MS-algebra is obtained. A one-to-one correspondence between the class of all balanced factor congruences of a double MS-algebra L and the central elements of L is obtained.
Highlights
Blyth and Varlet [1] introduced MS-algebras as a generalization of both de Morgan algebras and Stone algebras
We introduce the concept of central elements of a double MS-algebra L
We introduce the Birkhoof center of a double MS-algebra, we showed that the Birokhoof center of a double MS-algebra L can be identified with the center of L
Summary
Blyth and Varlet [1] introduced MS-algebras as a generalization of both de Morgan algebras and Stone algebras. We prove that the set of Stone elements of a double MS-algebra L forms the greatest Stone subalgebra of L. Factor congruences of a double MS-algebra are investigated by means of central elements.
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