Ideals and congruences in quasi-pseudo-MV algebras

Some Results in Weak Pseudo-Quasi-Wajsberg Algebras

“…For any quasi-pseudo-MV algebra, we introduced weak filters as a generalization of filters in [22]. All results can be paralleled to quasi-pseudo-Wajsberg algebras, especially, to pseudo-quasi-Wajsberg algebras.…”

“…In [22], we had proved that if A is a PQW-algebra and θ is a filter congruence on A, then F θ is a normal filter of A. In addition, if F is a normal filter of A and we define θ F = { a, b |a → b ∈ F and b → a ∈ F}, then θ F is a filter congruence on A.…”

“…To find more connections between weak PQW-algebras and other algebraic structures, we want to continue the investigation on weak PQW-algebras in this paper. It is well known that the basic tool for the investigation of algebraic structures is filter theory [7,[20][21][22][23]. On the one hand, the filters in connection with congruences on algebras are deeply investigated.…”