Relative ranks in the monoid of endomorphisms of an independence algebra

Normal Semigroups of Endomorphisms of Proper Independence Algebras are Idempotent Generated

Let X be a finite set. We denote by T (X) the monoid of all (total) transformations on X and by Sym(X) the symmetric group on X. An element a 2 T (X) \ Sym(X) is said to be singular. In 1966 Howie [4] proved that every singular transformation a 2 T (X) can be expressed as a product of idempotents of T (X). This result was generalized by Fountain and Lewin [2] for the case of independence algebr...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Affine Algebraic Monoids as Endomorphisms’ Monoids of Finite-dimensional Algebras

We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.

Endomorphisms of Relatively Free Algebras with Weak Exchange Properties

The structure of the endomorphism monoid of a stable basis algebra A is described. It is shown to be an abundant monoid; the subsemigroup of endomorphisms of finite rank has a regular semigroup of left quotients. This is a revised version of the article that appeared in Algebra Universalis 51 (2004), 257− −285. The authors are grateful to Professor George Bergman for correcting their original d...

Rank Properties of Endomorphisms of Infinite Partially Ordered Sets

The relative rank rank(S : U) of a subsemigroup U of a semigroup S is the minimum size of a set V ⊆ S such that U together with V generates the whole of S. As a consequence of a result by Sierpiński it follows that for U ≤ TX , the monoid of all self-maps of an infinite set X, rank(TX : U) is either 0, 1, 2 or uncountable. In this paper we consider the relative ranks rank(TX : OX), where X is a...