Let k be a p-adic field. It is well-known that k has only finitely many extensions of a given finite degree. In [Kr66], Krasner gives formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions K/k of a given degree and discriminant.

For each prime p and each embedding σ of the multiplicative group of an algebraic closure of Fp as complex roots of unity, we construct a p-adic indecomposable representation πσ of the integral BC-system as additive endomorphisms of the big Witt ring of F̄p. The obtained representations are the p-adic analogues of the complex, extremal KMS∞ states of the BC-system. The role of the Riemann zeta f...

Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of composition structure for (m,n)-hyperrings and study the connections with composition hyperrings. Moreover we show that particular strong endomorphisms of (m,n)-hyperrings can determine the composition structure of a such (m,n)-hyperrings. Finally, the three isomorphism theorems are pres...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Let k be a p-adic eld. It is well-known that k has only nitely many extension of a given nite degree. In Kr66], Krasner gives formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions K=k of a given degree and discriminant.

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

The aim of this paper is the study of fuzzy Γ-hyperrings. In this regard the notion of ν-fuzzy hyperideals of Γ-hyperrings are introduced and basic properties of them are investigated. In particular, the representation theorem for ν-fuzzy hyperideals are given and it is shown that the image of a ν-fuzzy hyperideal of a Γ-hyperring under a certain conditions is two-valued. Finally, the product o...