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

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, ...

For a cancellative semigroup S and field F, it is proved that the algebra FS centrally essential if only group of fractions GS exists FGS essential. The has classical right ring which ring. There exist non-commutative algebras over fields zero characteristic (this contrasts with known fact are commutative).