Stable rings generated by their units

Stable Rings Generated by Their Units

We introduce the class of rings satisfying (m,1)-stable range and investigate equivalent characterizations of such rings. These give generalizations of the corresponding results by Badawi (1994), Ehrlich (1976), and Fisher and Snider (1976). 2000 Mathematics Subject Classification. 19B10, 16E50. Let R be an associative ring with identity. A ring R is said to have stable range one provided that ...

Groups generated by two bicyclic units in integral group rings

A pr 2 00 9 Group Rings that are Additively Generated by Idempotents and Units

Let R be an Abelian exchange ring. We prove the following results: 1. RZ2 and RS3 are clean rings. 2. If G is a group of prime order p and p is in the Jacobson radical of R, then RG is clean. 3. If identity in R is a sum of two units and G is a locally finite group, then every element in RG is a sum of two units. 4. For any locally finite group G, RG has stable range one. All rings in this note...

Stable Models Are Generated by a Stable Chain

We propose a general preference criterion selecting thèintended' models of generalized logic programs which a) is a conservative extension of the stable model semantics for normal logic programs of GL88], b) is very close to the answer set semantics of GL91] for disjunctive logic programs, and c) allows for arbitrary formulas in the body and in the head of a rule, i.e. does not depend on the pr...

The Units of Group-rings

when addition and multiplication are defined in the obvious way, form a ring, the group-ring of G over K, which will be denoted by R (G, K). Henceforward, we suppose that K has the modulus 1, and we denote the identity in G by e0. Then R(G,K) has the modulus l.e0. Since no confusion can arise thereby, the element 1. e in R(G, K) will be written as e, and whenever it is convenient, the elements ...