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
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
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
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
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.
