The Isomorphism of Certain Continuous Rings

The isomorphism problem for commutative monoid rings’

By substantial changes and corrections in Demushkin’s old paper the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Z’ is obtained. This means that the underlying monoid is shown to be determined (up to isomorphism) by the corresponding monoid ring. Thereafter the positive answer to the analogous question for the ‘dual’ objects descrete Hodge algeb...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

On the Commütativity of Certain Rings

The isomorphism problem for monoid rings of rank 2 monoids *

The main result of this paper is that for a commutative ring R and finitely generated submonoids M and N of Z2 the monoid rings R [M] and R[N] are isomorphic as R algebras if and only if M and N are isomorphic. In the course of proof we derive various results concerning the structure of rank 2 monoids and isomorphisms between the corresponding monoid rings. 1991 Math. Subj. Class.: 13B25, 20M25...

The First Isomorphism Theorem and Other Properties of Rings

Different properties of rings and fields are discussed. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R −→ S we have R/ker(f) ∼= Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and h...