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 give a simple and unified proof showing that the unrestricted wreath product of weakly sofic, linear or hyperlinear group by an amenable is hyperlinear, respectively. By means Kaloujnine-Krasner theorem, this implies extensions with quotients preserve four aforementioned metric approximation properties. also discuss case co-amenable groups.

Defectless irreducible polynomials over a valued field (F, v) have been studied by means of strict systems of polynomial extensions and complete distinguished chains. Strong connections are developed here between these two approaches and applications made to both. In the tame case where a root α of an irreducible polynomial f generates a tamely ramified extension of (F, v), simple formulas are ...

In this article we give the definition of weakly prime hyperideals over multiplicative hyperring. We provide important results showing relations between and hyperideals. Then n-hyperideal (1,n) hyperideal hyperrings. investigate their properties some examples. Hyperstructures are very topic because it satisfy to study multidisiplinary. Especially in chemistry, coding theory, geometry, artificia...

Definition 1.1. If S is a multiplicative subset of a ring A (commutative with 1), the quotient hyperring A/mS = (A/mS,+, ·,−, 0, 1) is defined as follows: A/mS is the set of equivalence classes with respect to the equivalence relation ∼ on A defined by a ∼ b iff as = bt for some s, t ∈ S. The operations on A/mS are the obvious ones induced by the corresponding operations on A: Denote by a the e...