A multiplier on a normal subsemigroup of a group can be extended to a multiplier on the group. This is used to show that normal cancellative semigroups have the same second cohomology as the group they generate, generalising earlier results of Arveson, ChernofF, and Dinh. The main tool is a dilation theorem for isometric multiplier representations of semigroups.

Each factor semigroup of a free restriction (ample) semigroup over a congruence contained in the least cancellative congruence is proved to be embeddable into a W -product of a semilattice by a monoid. Consequently, it is established that each restriction semigroup has a proper (ample) cover embeddable into such a W -product.

We present new short proofs to both the exact and stability result of two extremal problems. The first is about extension Turán’s theorem hypergraphs, second cancellative hypergraphs. Our are concise straightforward, but give a sharper version theorems

Weighted automata and transducers are powerful devices used in many large-scale applications. The efficiency of these applications is substantially increased when the automata or transducers used are deterministic. There exists a general determinization algorithm for weighted automata and transducers that is an extension of the classical subset construction used in the case of unweighted finite...

We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with bracket either being quadratic or derived from a Lie algebra are cancellative. also use various invariants, including Makar–Limanov invariant, divisor subalgebra, and stratiform length, to skew algebras.

Gaussian or multivariate normal distributions are very popular and important probability models. Gaussian potentials [5] are multivariate normal density functions. Such a distribution is often given as a product of conditional Gaussian densities, which are more general than Gaussian potentials. These are related to Gaussian hints [11] and Gaussian belief functions [9, 10]. Gaussian potentials, ...

Condition $(PWP)$ which was introduced in (Laan, V., {it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $...