Multioperator algebras of Menger 
type (in Russian)

V.V. Varenyk

In the paper main derivative polylinear operations on $\Omega$-algebra over infinite field are considered. For the vector space, partial algebra-clone over the field is constructed and some of its properties are considered. We also found examples to illustrate the statements presented in the paper.

1. Cohn P.M. Universal algebra. – New York, Harper and Row, 1965.

2. Хион Я.В. $m$-арные $\Omega$-кольцоиды Сиб. мат. журн. -- 1967. -- Т.8, 194 1. -- C.174--194.

3. Артамонов В.А. Клоны полилинейных операций и мультиоператорные алгебры Усп. мат. наук. – 1969. – Т.24. – C.74–59.

4. Розенфельд Б.А. Многомерные пространства. – М.: Наука, 1966.

5. Калужнўн Л.А., Вишенський В.А., Шуб Ц.О. Лўнўйнў простори. – К.: Вища школа, 1971.

	Multioperator algebras of Menger type (in Russian)
Author	V.V. Varenyk Vinnytsia State Pedagogical University
Abstract	In the paper main derivative polylinear operations on $\Omega$-algebra over infinite field are considered. For the vector space, partial algebra-clone over the field is constructed and some of its properties are considered. We also found examples to illustrate the statements presented in the paper.
Keywords	derivative polylinear operations, infinite field, vector space, partial algebra-clone, algebraic structures, properties of algebra-clones, examples in algebra
DOI	doi:10.30970/ms.11.2.199-203
Reference	1. Cohn P.M. Universal algebra. – New York, Harper and Row, 1965. 2. Хион Я.В. $m$-арные $\Omega$-кольцоиды Сиб. мат. журн. -- 1967. -- Т.8, 194 1. -- C.174--194. 3. Артамонов В.А. Клоны полилинейных операций и мультиоператорные алгебры Усп. мат. наук. – 1969. – Т.24. – C.74–59. 4. Розенфельд Б.А. Многомерные пространства. – М.: Наука, 1966. 5. Калужнўн Л.А., Вишенський В.А., Шуб Ц.О. Лўнўйнў простори. – К.: Вища школа, 1971.
Pages	199-203
Volume	11
Issue	2
Year	1999
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Multioperator algebras of Menger type (in Russian)