Skip to main content
SpringerLink
Log in

Levi’s Commutator Theorems for Cancellative Semigroups

  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

For every semigroup of finite exponent whose chains of idempotents are uniformly bounded we construct an identity which holds on this semigroup but does not hold on the variety of all idempotent semigroups. This shows that the variety of all idempotent semigroups E is not contained in any finitely generated variety of semigroups. Since E is locally finite and each proper subvariety of E is finitely generated [1, 3, 4], the variety of all idempotent semigroups is a minimal example of an inherently non-finitely generated variety.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA

    Olga Sapir

Authors
  1. Olga Sapir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olga Sapir.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sapir, O. Levi’s Commutator Theorems for Cancellative Semigroups. Semigroup Forum 71, 140–146 (2005). https://doi.org/10.1007/s00233-004-0178-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-004-0178-1

Keywords

Search

Navigation