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2 results

  • A Representation Theorem for Distributive l-Monoids

  • Marlow Anderson, C. C. Edwards
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 2 / 01 June 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 238-240
    Print publication:
    01 June 1984
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  • In this note the Holland representation theorem for l-groups is extended to l-monoids by the following theorem: an l-monoid is distributive if and only if it may be embedded into the l-monoid of order-preserving functions on some totally ordered set. A corollary of this representation theorem is that a monoid is right orderable if and only if it is a subsemigroup of a distributive l-monoid; this result is analogous to the group theory case.

  • Lattice properties of the symmetric weakly inverse semigroup on a totally ordered set

  • Part of
  • C. C. Edwards, Marlow Anderson
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 31 / Issue 4 / December 1981
    Published online by Cambridge University Press:
    09 April 2009, pp. 395-404
    Print publication:
    December 1981
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  • Let T be a totally ordered set, PT the semigroup of partial transformations on T, and A(T) the l-group of order-preserving permutations of T. We show that PT is a regular left l-semigroup. Let be the set of α ∈ PT such that α is order-preserving and the domain of α is a final segment of T. Then is an l-semigroup, and we prove that it is the largest transitive l-subsemigroup of PT which contains A(T). When T is Dedekind complete, we characterize the largest regular l-semigroup of . When A(T) is also 0 − 2 transitive we show that there can be no l-subsemigroup of properly containing A(T) which is either inverse or a union of groups.