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 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.
