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2 results

  • Independence algebras, basis algebras and semigroups of quotients

  • Part of
  • Victoria Gould
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010
    Published online by Cambridge University Press:
    05 August 2010, pp. 697-729
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  • We show that if A is a stable basis algebra satisfying the distributivity condition, then B is a reduct of an independence algebra A having the same rank. If this rank is finite, then the endomorphism monoid of B is a left order in the endomorphism monoid of A.

  • PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF RELATIVELY FREE ALGEBRAS WITH WEAK EXCHANGE PROPERTIES

  • John Fountain, Victoria Gould
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 2 / June 2007
    Published online by Cambridge University Press:
    17 May 2007, pp. 343-362
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  • If $A$ is a stable basis algebra of rank $n$, then the set $S_{n-1}$ of endomorphisms of rank at most $n-1$ is a subsemigroup of the endomorphism monoid of $A$. This paper gives a number of necessary and sufficient conditions for $S_{n-1}$ to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left $T$-sets of finite rank, where $T$ is cancellative monoid in which every finitely generated left ideal is principal.