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Associativity of the ∇-operation on bands in rings

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Abstract

Given a multiplicative band of idempotents S in a ring R, for all e,f∈S the ∇-product e ∇ f=e+f+fe−efe−fef is an idempotent that lies roughly above e and f in R just as ef and fe lie roughly below e and f. In this paper we study ∇-bands in rings, that is, bands in rings that are closed under ∇, giving various criteria for ∇ to be associative, thus making the band a skew lattice. We also consider when a given band S in R generates a ∇-band.

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Authors and Affiliations

  1. Department of Mathematics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Karin Cvetko-Vah

  2. Department of Mathematics, Westmont College, 955 La Paz Road, Santa Barbara, CA, 93108, USA

    Jonathan Leech

Authors
  1. Karin Cvetko-Vah
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  2. Jonathan Leech
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Correspondence to Jonathan Leech.

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Communicated by Lászlo Márki

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Cvetko-Vah, K., Leech, J. Associativity of the ∇-operation on bands in rings. Semigroup Forum 76, 32–50 (2008). https://doi.org/10.1007/s00233-007-9007-7

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  • DOI: https://doi.org/10.1007/s00233-007-9007-7

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