Introduction. Several authors have established that many classical codes are ideals in certain ring constructions. Berman [3], in the case of characteristic two, and Charpin [5], in the general case, proved that all generalized Reed-Muller codes coincide with powers of the radical of the quotient ring A = Fq[x1, . . . , xn]/(x q1 1 − 1, . . . , xn n − 1), where Fq is a finite field, p = charFq ...

In this study, we define the concept of an ω-fuzzy set subring and show that intersection two subrings is also a given ring. Moreover, give notion ideal investigate different fundamental results phenomenon. We extend ideology to propose coset develop quotient ring with respect particular fuzzy analog into classical Additionally, found subring. idea support prove various important characteristic...

In this paper, we propose a weak version of quotient for the algebraic action group on variety, which shall call pseudo-quotient. They arise when focus purely topological properties good Geometric Invariant Theory (GIT) quotients regardless their properties. The flexibility granted by nature enables an easier identification in geometric constructions than classical GIT quotients. We obtain seve...

In this paper, we present different results related to bezoutian and residue theory. We consider, in particular, the problem of computing the structure of the quotient ring by an affine complete intersection, and an algorithm to obtain it, as conjectured in [9]. We analyze it in detail and prove the validity of the conjecture, for a modification of the initial method. Direct applications of the...

Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-rin...