Effective dimension of finite semigroups

TL;DR

This paper investigates the minimal dimension needed for an injective linear representation of finite semigroups, exploring techniques, results, and applications to various examples.

Contribution

It introduces new methods and insights for determining the effective dimension of finite semigroups in linear representations.

Findings

Developed techniques for calculating minimal dimensions

Applied methods to multiple finite semigroup examples

Provided bounds and exact values for specific cases

Abstract

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to numerous examples.