• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.945-959
• /
• 2008

n-ary $H_v$-structures is a generalisation of both n-ary structures and $H_v$-structures. A wide class of n-ary $P-H_v$-groups is the n-ary $P-H_v$-groups that is concidered in this paper. In this paper the notion of a normal subgroup of an n-ary $P-H_v$-groups is introduced and the isomorphism theorems for n-ary $P-H_v$-groups are stated and proved. Also some examples and related properties are investigated.

• 대한수학회보
• /
• 제50권2호
• /
• pp.507-524
• /
• 2013

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

• East Asian mathematical journal
• /
• 제21권2호
• /
• pp.241-248
• /
• 2005

Properties of congruences on n-ary groups are investigated.

• East Asian mathematical journal
• /
• 제19권1호
• /
• pp.63-71
• /
• 2003

In his invited lecture presented during the First Conference of the Mathematical Society of the Republic of Moldova($Chi\c{s}in\v{a}u$, August 2001) W. A. Dudek posed several open problems on the role and properties of the skew element in the theory of n-ary groups. In this note we give the partial solutions of some of these problems.