G. Bergman

works on

dimension inequalities 1 order theory 1 poset dimension 1 poset relations 1 product posets 1

From the 1 of 7 linked papers with an AI index.

collaborators

7 papers

math.GR2026

An observation on factorizations of finite groups

George M. Bergman

Given a finite group $G$ and a factorization of its order, $∣ G ∣ = a_{1} a_{2},$ we show that a sufficient condition for there to exist subsets $A_{1}, A_{2} \subseteq G$ such that $|A_1| =…

math.CO2026

Further thoughts on dimensions of posets

George M. Bergman

The paper reviews the concept of dimension for finite posets, discusses a longstanding conjecture about the dimension of product posets, proposes two related inequalities, and intr…

math.GR2026

Criteria for existence of semigroup homomorphisms and projective rank functions

George M. Bergman

Let $P,$ $S,$ and $T$ be semigroups, $f : P \to S$ and $g : P \to T$ semigroup homomorphisms, and $X$ a generating set for $S$ (possibly infinite). Clearly, a <i>necessary</i> condition…

math.CO2025

Some frustrating questions on dimensions of products of posets

George M. Bergman

For $P$ a poset, the dimension of $P$ is defined to be the least cardinal $I^º$ such that $P$ is embeddable in a direct product of $I^º$ totally ordered sets. We study the behavior o…

math.RA2025

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 $C$ is a category of algebras closed under finite direct products, and $M_{C}$ the commutative monoid of isomorphism classes of members of $C,$ with…

math.GR2025

Adjoining universal inverses to families of elements of free monoids

George M. Bergman

Let $< X >$ be the free monoid on a generating set $X$ , and suppose one adjoins to $< X >$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorit…