Serial rings and subdirect products

Subdirect Sums of Rings

Subdirect Products of Semirings

Bandelt and Petrich (1982) proved that an inversive semiring S is a subdirect product of a distributive lattice and a ring if and only if S satisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, ...

Maximal n-generated subdirect products

For n a positive integer and K a finite set of finite algebras, let L(n,K) denote the largest n-generated subdirect product whose subdirect factors are algebras in K. When K is the set of all ngenerated subdirectly irreducible algebras in a locally finite variety V, then L(n,K) is the free algebra FV(n) on n free generators for V. For a finite algebra A the algebra L(n, {A}) is the largest n-ge...

Note on Subdirect Sums of Rings

where (a) denotes the two-sided ideal of R generated by a. Then J is the Jacobson radical [6 ] of R, and N is the radical of R as defined in [l]. It is well known that J = 0 if and only if R is isomorphic to a subdirect sum of primitive rings, and ^ = 0 if and only if R is isomorphic to a subdirect sum of simple rings with unit element. The above definitions of / and N suggest that it might be ...

Completely Subdirect Products of Directed Sets

This paper deals with directly indecomposable direct factors of a directed set.