Let G be an abelian group with identity e. R a graded multiplicative hyperring and ? : Igr(R) expansion function of Igr(R), where is the set all hyperideals R. In this paper, we introduce study concepts ?-primary 2-absorbing which are extended classes prime 2- absorbing R, respectively. Moreover, give basic properties these new types investigate relations among structures.

We consider three notions of factorization arising in different frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X ⊆ A∗ is called factorizing if there exists a language Y ⊆ A∗ such that XY = A∗ and the product is unambiguous. This is a decidable property for recognizable languages X . If we consider the particular case of unary alphabets, we...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and primary of a Krasner (m,n) $-hyperring, including hyperideal hyperideal. Therefore, give generalizations Also, examine the relations between classical explore some ways to connect them. Additionally, main results examples are given explain structures these concepts. Finally, study version Nakaya...

An M-polysymmetrical hyperring $(R,+,cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,cdot )$ is a semigroup and $cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphi...

In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

The wreath product of groups A B is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras H and G over a field K. Let U(G) be the universal enveloping algebra. Then H̄ = HomK(U(G), H) has the natural structure of a Lie algebra, where the multiplication is defined via the comultiplication in U(G). Also, G acts by derivations...