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A semigroup embedding problem and an arithmetical function

  • John M. Howie (a1) and J. L. Selfridge (a2)

For unexplained terms in semigroup theory see [1] or [4].

Let C, D be classes of semigroups such that every finite semigroup in the class C is embeddable in a finite semigroup in the class D. If n ≥ 2 then k is said to be a CDcover of n if every semigroup of order n in the class C is embeddable in a semigroup in the class D of order not greater than k. Let be the least CD cover of n.

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[1]Clifford A. H. and Preston G. B.. The algebraic theory of semigroups, vol. 1. Math. Surveys no. 7 (American Mathematical Society, 1961).
[2]Giraldes E.. Semigroups of high rank. II. Doubly noble semigroups. Proc. Edinburgh Math. Soc. (2) 28 (1985), 409417.
[3]Giraldes E. and Howie John M.. Semigroups of high rank. Proc. Edinburgh Math. Soc. (2) 28 (1985), 1334.
[4]Howie John M.. An Introduction to Semigroup Theory (Academic Press, 1976).
[5]Howie John M.. Idempotents in completely 0-simple semigroups. Glasgow Math. J. 19 (1978), 109113.
[6]Howie John M.. Embedding semigroups in semibands; some arithmetical results. Quart. J. Math. Oxford Ser. (2) 32 (1981), 323337.
[7]Howie John M.. Arithmetical aspects of semigroup embeddings. In Proceedings Lisbon Conference on Lattices, Semigroups and Universal Algebra. (To appear.)
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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