Generalized morphisms of abelian m-ary groups
Discussiones Mathematicae - General Algebra and Applications (2001)
- Volume: 21, Issue: 1, page 47-55
- ISSN: 1509-9415
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topAlexander M. Gal'mak. "Generalized morphisms of abelian m-ary groups." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 47-55. <http://eudml.org/doc/287594>.
@article{AlexanderM2001,
abstract = {We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.},
author = {Alexander M. Gal'mak},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {n-ary endomorphism; m-ary group; (m,n)-ring; -ary groups; homomorphisms; -rings; endomorphisms},
language = {eng},
number = {1},
pages = {47-55},
title = {Generalized morphisms of abelian m-ary groups},
url = {http://eudml.org/doc/287594},
volume = {21},
year = {2001},
}
TY - JOUR
AU - Alexander M. Gal'mak
TI - Generalized morphisms of abelian m-ary groups
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 47
EP - 55
AB - We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
LA - eng
KW - n-ary endomorphism; m-ary group; (m,n)-ring; -ary groups; homomorphisms; -rings; endomorphisms
UR - http://eudml.org/doc/287594
ER -
References
top- [1] G. Crombez, On (n, m)-rings, Abh. Math. Sem. Univ. Hamburg 37 (1972), 180-199. Zbl0247.08001
- [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, 'Proc. Symp. on n-ary Structures (Skopje 1982)', Macedonian Academy of Sciences and Arts, Skopje 1982, 253-289. Zbl0582.20057
- [4] K. Głazek and B. Gleichgewicht, Abelian n-groups, Colloq. Math. Soc. J. Bolyai, no. 29 ('Universal Algebra, Esztergom (Hungary) 1977'), North-Holland, Amsterdam 1981, 321-329.
- [5] E.L. Post, Polyadic groups, Trans. Amer. Math. Soc. 48 (1940), 208-350. Zbl66.0099.01
- [6] S.A. Rusakov, Sequences of mappings and the existence of symmetric n-ary groups (Russian), 'The Arithmetic and Subgroup Structure of Finite Groups' (Russian), Navuka i Tehnika, Minsk 1986, 120-134.
- [7] S.A. Rusakov, Algebraic n-ary systems (Russian), Navuka i Tehnika, Minsk 1992.
- [8] J. Timm, Kommutative n-Gruppen, Dissertation, Univ. Hamburg 1967.
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