This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers...This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities;the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded distributive lattice of n-ary monotone Boolean functions;the functional representations of finitely-generated free algebras of various varieties of lattices via generalized Boolean functions, etc.展开更多
The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan alge...The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan algebra, （L; ∧ , ∨ , , ＋ , 0, 1） is a double demi-p-lattice and the operations x → x , x → x and x → x ＋ are linked by the identities x = x , x ＋ = x ＋ and x ＋ = x ＋ . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.展开更多
In this work we review the class T of ternary algebras introduced by J. A. Brzozowski and C. J. Serger in [1]. We determine properties of the congruence lattice of a ternary algebra A. The most important result refers...In this work we review the class T of ternary algebras introduced by J. A. Brzozowski and C. J. Serger in [1]. We determine properties of the congruence lattice of a ternary algebra A. The most important result refers to the construction of the free ternary algebra on a poset. In particular, we describe the poset of the join irreducible elements of the free ternary algebra with two free generators.展开更多
In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated b...In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated by R. Sikorski for finite Boolean algebras [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100310038000000 , and by M. Abad and A. V. Figallo for finite 3-valued ukasiewicz algebras [2] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100320031000000 .展开更多
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
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
文摘This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities;the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded distributive lattice of n-ary monotone Boolean functions;the functional representations of finitely-generated free algebras of various varieties of lattices via generalized Boolean functions, etc.
文摘The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan algebra, （L; ∧ , ∨ , , ＋ , 0, 1） is a double demi-p-lattice and the operations x → x , x → x and x → x ＋ are linked by the identities x = x , x ＋ = x ＋ and x ＋ = x ＋ . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.
文摘In this work we review the class T of ternary algebras introduced by J. A. Brzozowski and C. J. Serger in [1]. We determine properties of the congruence lattice of a ternary algebra A. The most important result refers to the construction of the free ternary algebra on a poset. In particular, we describe the poset of the join irreducible elements of the free ternary algebra with two free generators.
文摘In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated by R. Sikorski for finite Boolean algebras [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100310038000000 , and by M. Abad and A. V. Figallo for finite 3-valued ukasiewicz algebras [2] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100320031000000 .
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.
