in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...

This is a sequel to [Li4] and [Li5] in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian DY~(sl2), denoted by DYq(sl2) and DY ∞ q (sl2) with q a nonzero complex number. For each nonzero complex number q, we construct a quantum vertex algebra Vq and prove that eve...

The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers. The product bases of that group are represented by the multiplicative group of invertible elements in that matrix ring. All products in the Baer-Specker group are characterized, and a lemma of László Fuchs regarding such products i...

Research on gender differences in creativity, including creativity test scores, creative achievements, and self-reported creativity is reviewed, as are theories that have been offered to explain such differences and available evidence that supports or refutes such theories. This is a difficult arena in which to conduct research, but there is a consistent lack of gender differences both in creat...