On exact category of $(m, n)$-ary hypermodules

Canonical (m,n)−ary hypermodules over Krasner (m,n)−ary hyperrings

The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...

Exact category of hypermodules

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

STRONGLY TRANSITIVE GEOMETRIC SPACES ASSOCIATED WITH (m,n)-ARY HYPERMODULES

In this paper, we define the strongly compatible relation ε on the (m,n)ary hypermodule M, so that the quotient (M/ε∗, h/ε∗) is an (m,n)-ary module over the fundamental (m,n)-ary ring (R/Γ∗, f/Γ∗, g/Γ∗). Also, we determine a family P (M) of subsets of an (m,n)-ary hypermodule M and we give a sufficient condition such that the geometric space (M,P (M)) is strongly transitive. Mathematics Subject...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

The Number of m-ary Search Trees on n Keys

24 Let h(x) := log 2 x x ?2 log(x + 1) expff(x)g = x log 2 ? 2 log x + log log(x + 1) + f(x); it suuces to show that h(x) > 0 for x 5. Now h(5) : = 0:20 > 0 and h 0 (x) = log 2 ? 2x ?1 + 1 (x + 1) log(x + 1) + (x ? 1) ?2 log x > 1 (x + 1) log(x + 1) + (x ? 1) ?2 log x > 0 for x 5. Thus h(x) > 0 for x 5. This follows from calculus, since the last expression is strictly increasing in real m > 1.

on $n$-ary hypergroups and fuzzy $n$-ary homomorphism