ON CONVOLUTION TYPES IN COMMUTATIVE RINGS

On Convolution Types in Commutative Rings

For a commutative associate unital ring R the notion of an Rconvolution type is introduced and applied to R-algebras. Some examples are presented and relations to known concepts are discussed. Mathematics Subject Classification (2010): 16S99, 13F99, 13F20, 13F25

ON COMMUTATIVE GELFAND RINGS

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

On Commutative Reduced Baer Rings

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

Deformations of Convolution Semigroups on Commutative Hypergroups

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...

Factorization in Commutative Rings