# zbMATH — the first resource for mathematics

Homomorphisms of heterogeneous algebras. (English) Zbl 1016.08005
Summary: 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 a previous paper of the author [Czech. Math. J. 52, 345-364 (2002; Zbl 1010.08004)].

##### MSC:
 08A68 Heterogeneous algebras 08A02 Relational systems, laws of composition 08C05 Categories of algebras
Full Text:
##### References:
 [1] G. Birkhoff and J. D. Lipson: Heterogeneous algebras. J. Combin. Theory 8 (1970), 115-133. · Zbl 0211.02003 [2] P. M. Cohn: Universal Algebra. Harper and Row, New York-Evanston-London, 1965. · Zbl 0141.01002 [3] J. A. Goguen, J. W. Thatcher, E. G. Wagner and J. B. Wright: Initial algebra semantics and continuous algebras. J. Assoc. Comput. Mach. 24 (1977), 68-95. · Zbl 0359.68018 [4] P. J. Higgins: Algebras with a schema of operators. Math. Nachr. 27 (1963), 115-132. · Zbl 0117.25903 [5] A. A. Letičevskij: Sintaksis i semantika formal’nych jazykov (Syntax and semantics of formal languages). Kibernetika No 4, 1968, pp. 1-9. [6] S. Mac Lane: Categories for the Working Mathematician. Springer, New York-Heidelberg-Berlin, 1971. · Zbl 0232.18001 [7] M. Novotný: Sur un problème de la théorie des applications. Publ. Fac. Sci. Univ. Masaryk Brno No 344 (1953/2), 53-64. [8] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians. Arch. Math. (Brno) 26 (1990), 155-164. · Zbl 0741.08001 [9] M. Novotný: On some correspondences between relational structures and algebras. Czechoslovak Math. J. 43 (118) (1993), 643-647. · Zbl 0794.08009 [10] M. Novotný: Construction of all homomorphisms of mono-$$n$$-ary algebras. Czechoslovak Math. J. 46 (121) (1996), 331-333. · Zbl 0870.08005 [11] M. Novotný: Homomorphisms of algebras. Czechoslovak Math. J 52 (127) (2002), 345-364. · Zbl 1010.08004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.