Skip to main content

Hereditarily Finitely Based Varieties of Monoids

  • Chapter
  • First Online:
Advances in the Theory of Varieties of Semigroups

Part of the book series: Frontiers in Mathematics ((FM))

  • 172 Accesses

Abstract

The existence and uniqueness of two maximal hereditarily finitely based overcommutative varieties of monoids are established. A characterization of hereditarily finitely based varieties of monoids from several large classes is then given.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • T.J. Head, The varieties of commutative monoids. Nieuw Arch. Wisk. (3) 16, 203–206 (1968)

    Google Scholar 

  • G. Higman, Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2(1), 326–336 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  • M. Jackson, Finiteness properties of varieties and the restriction to finite algebras. Semigroup Forum 70(2), 159–187 (2005b)

    Article  MathSciNet  MATH  Google Scholar 

  • E.W.H. Lee, Maximal Specht varieties of monoids. Mosc. Math. J. 12(4), 787–802 (2012b)

    Article  MathSciNet  MATH  Google Scholar 

  • M.V. Volkov, A general finite basis condition for systems of semigroup identities. Semigroup Forum 41(2), 181–191 (1990)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lee, E.W.H. (2023). Hereditarily Finitely Based Varieties of Monoids. In: Advances in the Theory of Varieties of Semigroups. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-16497-2_11

Download citation

Publish with us

Policies and ethics