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Transformation semigroups associated to Γ-semigroups

Dariush Heidari, Marzieh Amooshahi (2013)

Discussiones Mathematicae - General Algebra and Applications

The concept of Γ-semigroups is a generalization of semigroups. In this paper, we associate two transformation semigroups to a Γ-semigroup and we call them the left and right transformation semigroups. We prove some relationships between the ideals of a Γ-semigroup and the ideals of its left and right transformation semigroups. Finally, we study some relationships between Green's equivalence relations of a Γ-semigroup and its left (right) transformation semigroup.

Transformations determining uniquely a monoid

Marie Münzová-Demlová (1970)

Commentationes Mathematicae Universitatis Carolinae

Transformations determining uniquely a monoid. II.

Marie Münzová-Demlová (1974)

Commentationes Mathematicae Universitatis Carolinae

Transformations determining uniquely a monoid. III: Weak determinancy

Marie Münzová-Demlová (1975)

Commentationes Mathematicae Universitatis Carolinae

Transformations determining uniquely a monoid. IV: Weak determinancy

Marie Münzová-Demlová (1975)

Commentationes Mathematicae Universitatis Carolinae

Transformations in a three-space.

Edward D. Bender, John G. Christiano (1964)

Bollettino dell'Unione Matematica Italiana

Transience of algebraic varieties in linear groups - applications to generic Zariski density

Richard Aoun (2013)

Annales de l’institut Fourier

We study the transience of algebraic varieties in linear groups. In particular, we show that a “non elementary” random walk in $S L_{2} (ℝ)$ escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk takes place in the real points of a semisimple split algebraic group and show such a result for a wide family of random walks.As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.