Β-Filters OF MS-ALGEBRAS

Abstract

The concepts of boosters and β-filters are introduced in an MS -algebra and the β-filters are characterized in terms of boosters. It is then proved that the lattice of β-filters is isomorphic to the ideal lattice of the lattice of boosters. A set of equivalent conditions are derived for the lattice of boosters to become a relatively complemented lattice.

Boosters and Filters in MS-Almost Distributive Lattices

“…Let D be a filter of an MS-algebra A. Rao in [8] defined that D is said to be an e-filter of A whenever D = D e , where The concept of β-filter of MS-algebra is given by Rao [8]. Next, we extend the concept of this filter to β-filters of MS-ADLs.…”

“…The class of all MS-algebras forms an equational class. The subvarieties of MS-algebras is characterized by Blyth and Varlet [4], and Rao [8] studied about β-filter of MS-Algebra.…”

Extended Filters of MS -Algebras

“…The class MS is a subclass of Berman class K 1,1 which introduced by Berman in [3]. The theory of filters such as d L -filters [1] and β-filters [12] of MS-algebras has been studied by many authors. In the twenty-first century, many related structures to lattice theory and MS-algebras [10,11] had a great concern.…”