52 citations · 217 across the 45 of their papers we have counts for
23 papers · 1 filter
Strongly clean ring elements that are one-sided inverses
George M. Bergman
A longstanding open question is whether every strongly clean ring (ring in which every element is strongly clean, i.e., is the sum of an idempotent and a unit which commute with ea…
On semigroups that are prime in the sense of Tarski, and groups prime in the senses of Tarski and of Rhodes
George M. Bergman
If is a category of algebras closed under finite direct products, and the commutative monoid of isomorphism classes of members of with…
An elementary result on infinite and finite direct sums of modules
George M. Bergman
Let be a ring, and consider a left -module given with two (generally infinite) direct sum decompositions, $A\oplus(\bigoplus_{i\in I} C_i)=M=B\oplus(\bigoplus_{j\in J} D_j),…
Some embedding results for associative algebras
George M. Bergman
Suppose we wish to embed an (associative) -algebra in a -algebra generated in some specified way; e.g., by two elements, or by copies of given -algebras $A_…
Some results relevant to embeddability of rings (especially group algebras) in division rings
George M. Bergman
P. M. Cohn showed in 1971 that given a ring , to describe, up to isomorphism, a division ring generated by a homomorphic image of is equivalent to specifying the set of…
Completeness results for metrized rings and lattices
George M. Bergman
The Boolean ring of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (e.g., that are closed under the natural metric, bu…