A nonlinear stochastic equation in a Hilbert space is considered, with constant but possibly degenerate diiusion term. Some smoothing properties for the associated transition semigroup are studied. In particular, strong Feller property and irreducibility are proved. The main tools are Malliavin calculus and Girsanov transformation.

We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...

Using a variant of Schreier’s Theorem, and the theory of Green’s relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids...

Let S be a semigroup. The elements a, b ∈ S are called primarily conjugate if a = xy and b = yx for certain x, y ∈ S. The relation of conjugacy is defined as the transitive closure of the relation of primary conjugacy. In the case when S is a monoid, denote by G the group of units of S. Then the relation of G-conjugacy is defined by a ∼G b ⇐⇒ a = gbg for certain g ∈ G. We establish the structur...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).