The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice ...The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice endomorphism on L with x≤x^(+)=x^(++)and the operations x→x°,x→x^(*)and x→x^(+)are linked by the identities x^(+*)=x^(*+)and x^(+)°=x°^(+).In this paper,we characterize congruences on a CPMS-algebra,and show that there are precisely eight non-isomorphic subdirectly irreducible nontrivial algebras in the class of these algebras and give a complete description of them.展开更多
The variety bpO consists of those algebras （L; ∧,∨, f,＊ ） of type 〈2,2,1, 1,0,0〉 where （L; ∧,∨, f, 0, 1） is an Ockham algebra, （L; ∧,∨, ＊, 0, 1） is a p-algebra, and the operations x → f（x） and x →...The variety bpO consists of those algebras （L; ∧,∨, f,＊ ） of type 〈2,2,1, 1,0,0〉 where （L; ∧,∨, f, 0, 1） is an Ockham algebra, （L; ∧,∨, ＊, 0, 1） is a p-algebra, and the operations x → f（x） and x → x^＊ satisfy the identities f（x^＊） = x^＊＊ and [f（x）]^＊ = f^2（x）. In this note, we show that the compact congruences on a bpO-algebra form a dual Stone lattice. Using this, we characterize the algebras in which every principal congruence is complemented. We also give a description of congruence coherent bpO-algebras.展开更多
文摘The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice endomorphism on L with x≤x^(+)=x^(++)and the operations x→x°,x→x^(*)and x→x^(+)are linked by the identities x^(+*)=x^(*+)and x^(+)°=x°^(+).In this paper,we characterize congruences on a CPMS-algebra,and show that there are precisely eight non-isomorphic subdirectly irreducible nontrivial algebras in the class of these algebras and give a complete description of them.
文摘The variety bpO consists of those algebras （L; ∧,∨, f,＊ ） of type 〈2,2,1, 1,0,0〉 where （L; ∧,∨, f, 0, 1） is an Ockham algebra, （L; ∧,∨, ＊, 0, 1） is a p-algebra, and the operations x → f（x） and x → x^＊ satisfy the identities f（x^＊） = x^＊＊ and [f（x）]^＊ = f^2（x）. In this note, we show that the compact congruences on a bpO-algebra form a dual Stone lattice. Using this, we characterize the algebras in which every principal congruence is complemented. We also give a description of congruence coherent bpO-algebras.
