52 citations · 217 across the 45 of their papers we have counts for
52 papers
An observation on factorizations of finite groups
George M. Bergman
Given a finite group and a factorization of its order, we show that a sufficient condition for there to exist subsets such that $|A_1| =…
Further thoughts on dimensions of posets
George M. Bergman
We recall the concept of the dimension of a finite poset , and the longstanding conjecture that for all finite nonempty posets and , $\dim(P\times Q)\geq\dim(P)+\dim(Q)-2…
Criteria for existence of semigroup homomorphisms and projective rank functions
George M. Bergman
Let and be semigroups, and semigroup homomorphisms, and a generating set for (possibly infinite). Clearly, a <i>necessary</i> condition…
Adjoining universal inverses to families of elements of free monoids
George M. Bergman
Let be the free monoid on a generating set , and suppose one adjoins to universal 2-sided inverses to a finite set of its elements. We note an elementary algorit…
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…