Homomorphisms of algebras

A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra with a finite number of operations into an algebra of the same type can be described.     

Homomorphisms of heterogeneous algebras

A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].     

Partition theorems for unary algebras

Those unary algebras (A, ?) (A a set, ? a mapping from A into A) are characterized for which an analog of Ramsey's theorem holds.     

Quasiidentities of finite unary algebras

Translated from Algebra i Logika, Vol. 28, No. 5, pp. 493–512, September–October, 1989.     

Semivarieties and Schreier varieties of unary algebras

A correction is provided for one result of a paper by Shafaat [1], and it is proven that the set of Schreier varieties of algebras 〈A;⁺1〉 with two unary operations has the cardinality of the continuum.     

Power algebras and generalized quotient algebras

The notion of a good quotient relation has been introduced as an attempt to generalize the notion of a quotient algebra to relations on an algebra which are not necessarily congruences. In order to make it possible to prove generalized versions of 'power isomorphism theorems', the more restrictive notions of very good, Hoare good and Smyth good relation have been introduced. In this paper we describe the relationships between Hoare good, Smyth good and very good relations. As a consequence, we prove that every structure preserving relation on an algebra is very good. Received September 25, 1998; accepted in final form January 14, 1999.     

Homomorphisms on some function algebras

In this note we prove, for some classes of real locally convex spacesE including all complete Schwartz spaces, that every non-zero homomorphism on the algebraC (E) ofC -functions onE is given by a point evaluation at some point ofE.     

On commutative unary algebras with totally ordered congruence lattice

The class of all commutative unary algebras (with arbitrarily many operations) with totally ordered congruence lattice is described.     

Homomorphisms onto effectively separable algebras

We study variations of the concept of separable enumeration and, basing on that, describe a series of algorithmic and algebraic concepts. In this framework we characterize negative equivalences, describe enumerated algebras with the most general separability conditions, give a separability criterion for the enumerated algebras satisfying the descending chain condition for the lattices of congruences, and consider some questions related to the algorithmic complexity of enumerations of the algebras satisfying various separability axioms.     

Homomorphisms in quasi-Banach algebras associated with a Pexiderized Cauchy-Jensen functional equation

In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation
f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.
This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.     

Homomorphisms of certain Banach function algebras

In this note, we study homomorphisms with domainD ⁿ(X) orLipα(X, d) of which ranges are certain Banach function algebras and determine in which cases these homomorphisms are compact.