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Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 47-55
DOI: https://doi.org/10.7151/dmgaa.1026

GENERALIZED MORPHISMS OF ABELIAN m-ARY GROUPS

A M. Gal'mak

Department of Mathematics, Technological Institute
Shmidt ave. 3, 212027 Mogilev, Belarus

Abstract

We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m, n) - ring.

Keywords and phrases: n-ary endomorphism, m-ary group, (m, n)-ring.

2000 Mathematics Subject Classification: Primary 20N15; Secondary 16Y99.

References

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[2]	A.M. Gal'mak, Generalized morphisms of algebraic systems (Russian), Voprosy Algebry 12 (1998), 36-46.
[3]	K. Głazek, Bibliography of n-groups (polyadic groups) and some group-like n-ary systems, p. 253-289 in: `` Proc. Symp. on n-ary Structures (Skopje 1982)", Macedonian Academy of Sciences and Arts, Skopje 1982.
[4]	K. Głazek and B. Gleichgewicht, Abelian n-groups, p. 321-329 in: Colloq. Math. Soc. J. Bolyai, no. 29 (``Universal Algebra, Esztergom (Hungary) 1977"), North-Holland, Amsterdam 1981.
[5]	E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350.
[6]	S.A. Rusakov, Sequences of mappings and the existence of symmetric n-ary groups (Russian), p. 120-134 in: ``The Arithmetic and Subgroup Structure of Finite Groups" (Russian), Navuka i Tehnika, Minsk 1986.
[7]	S.A. Rusakov, Algebraic n-ary systems (Russian), Navuka i Tehnika, Minsk 1992.
[8]	J. Timm, Kommutative n-Gruppen, Dissertation, Univ. Hamburg 1967.

Received 27 June 1999
Revised 22 September 1999
Revised 2 August 2000
Revised 5 March 2001