An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP （that...An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP （that is, endomorphism kernel property） for an extended Ockham algebra A. In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP.展开更多
Here we introduce a subclass of the class of Ockham algebras （L; f） for which L satisfies the property that for every x ∈ L, there exists n 〉 0 such that fn（x） and f^n＋1（x） are complementary. We characterize ...Here we introduce a subclass of the class of Ockham algebras （L; f） for which L satisfies the property that for every x ∈ L, there exists n 〉 0 such that fn（x） and f^n＋1（x） are complementary. We characterize the structure of the lattice of congruences on such an algebra （L; f）. We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains.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
Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained ...Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.展开更多
The variety eO of extended Ockham algebras consists of those algebras （L; ∧, ∨, f, k, 0, 1） such that （L; ∧, ∨, 0, 1） is a bounded distributive lattice together with a dual endomorphism f on L and an endomorp...The variety eO of extended Ockham algebras consists of those algebras （L; ∧, ∨, f, k, 0, 1） such that （L; ∧, ∨, 0, 1） is a bounded distributive lattice together with a dual endomorphism f on L and an endomorphism k on L such that fk = kf. In this paper we extend Urquhart＇s theorem to eO-algebras and we are in particular concerned with the subclass e2M of eO-algebras in which f^2 = id and k^2 = id. We show that there are 19 non-equivalent axioms in e2M and then order them by implication.展开更多
In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i<...In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i</sub>（i=1, 2,…,n） exists if and only if L<sub>1</sub>,...,L<sub>n</sub> have isomorphic skeletons.展开更多
An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.
In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are ...In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.展开更多
An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-alg...An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.展开更多
In this note, we study of those congruences on an Ockham algebra with de Morgan skeleton that the quotient algebras belong to the class of de Morgan algebras. We particularly give a description of those kernel ideals ...In this note, we study of those congruences on an Ockham algebra with de Morgan skeleton that the quotient algebras belong to the class of de Morgan algebras. We particularly give a description of those kernel ideals that generate these congruences.展开更多
文摘An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP （that is, endomorphism kernel property） for an extended Ockham algebra A. In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP.
文摘Here we introduce a subclass of the class of Ockham algebras （L; f） for which L satisfies the property that for every x ∈ L, there exists n 〉 0 such that fn（x） and f^n＋1（x） are complementary. We characterize the structure of the lattice of congruences on such an algebra （L; f）. We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains.
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.
文摘Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.
文摘The variety eO of extended Ockham algebras consists of those algebras （L; ∧, ∨, f, k, 0, 1） such that （L; ∧, ∨, 0, 1） is a bounded distributive lattice together with a dual endomorphism f on L and an endomorphism k on L such that fk = kf. In this paper we extend Urquhart＇s theorem to eO-algebras and we are in particular concerned with the subclass e2M of eO-algebras in which f^2 = id and k^2 = id. We show that there are 19 non-equivalent axioms in e2M and then order them by implication.
文摘In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i</sub>（i=1, 2,…,n） exists if and only if L<sub>1</sub>,...,L<sub>n</sub> have isomorphic skeletons.
文摘An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.
文摘In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.
文摘An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.
文摘In this note, we study of those congruences on an Ockham algebra with de Morgan skeleton that the quotient algebras belong to the class of de Morgan algebras. We particularly give a description of those kernel ideals that generate these congruences.
