We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical ...

Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, ...

ABSTRACT In this work, we introduce a method by which it is established that how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling ...

In this paper, we present constructions of primitive and non-primitive BCH codes using monoid rings over the local ring Z(2m), with m >= 1. We show that there exist two sequences {C-bjn}(j >= 1). and {C'(bjn)}(j >= 1) of ...

We show that if X is a toric scheme over a regular commutative ring k then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was previously ...

The aim of this work is to study the finiteness of the effective monoids and Cox rings of some anticanonical rational surfaces whose Picard numbers are very high and which are constructed as the blow-up of a Hirzebruch ...

Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Grabner bases can be characterized by properties of ...

We show that if X is a toric scheme over a regular ring containing a field of finite characteristic, then the direct limit of the K-groups of X taken over any infinite sequence of non-trivial dilations is homotopy invariant. ...