EQ-algebras with internal states

作者：Wang, Wei; Xin, Xiao Long^*; Wang, Jun Tao

来源：Soft Computing, 2018, 22(9): 2825-2841.

DOI：10.1007/s00500-017-2754-9

• SEQ-algebra
• S-prefilter
• S-filter
• sigma-Co-annihilator
• Representable

The main goal of this paper is to investigate EQ-algebras with internal states and state morphism good EQ-algebras. To begin with, we introduce the notion of EQ-algebras with internal states (simplify, SEQ-algebras) and discuss the relation between SEQ-algebras and state EQ-algebras. In the following, we study state filters (simplify, S-filters) and state prefilters (simplify, S-prefilters) of SEQ-algebras and discuss subdirectly irreducible SEQ-algebras. We focus on algebraic structures of the set SPF of all S-prefilters on a SEQ-algebra and obtain that SPF forms a complete Brouwerian lattice, when E is an EQ-algebra or good. Moreover, for EQ-algebras, SPF forms a Heyting algebra if is faithful and preserves . Then, we introduce the -co-annihilator of a non-empty set A on a SEQ-algebra. As applications, we give a characterization for minimal prime S-prefilters of state morphism good EQ-algebras and characterize the representable state morphism good EQ-algebras by minimal prime S-prefilters.

• 出版日期2018-5
• 单位西北大学