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The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue


Trotter, PG and Weil, P, The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue, Algebra Universalis, 37, (4) pp. 491-526. ISSN 0002-5240 (1997) [Refereed Article]

DOI: doi:10.1007/s000120050033


We use classical results on the lattice ℒ (ℬ) of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice Ps(DA) of subpseudovarieties of DA, - where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. We bring forward a lattice congruence on Ps(DA), whose quotient is isomorphic to ℒ(ℬ), and whose classes are intervals with effectively computable least and greatest members. Also we characterize the pro-identities satisfied by the members of an important family of subpseudovarieties of DA. Finally, letting Vk be the pseudovariety generated by the k -generated elements of DA (k ≥ 1), we use all our results to compute the position of the congruence class of Vk in ℒ(ℬ).

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Trotter, PG (Dr Peter Trotter)
UTAS Author:Weil, P (Professor Weil)
ID Code:11523
Year Published:1997
Web of Science® Times Cited:16
Deposited By:Mathematics
Deposited On:1997-08-01
Last Modified:2011-08-12

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