Through a method given in [3], a mixed partition of PG(2n− 1, q2) can be used to construct a (2n− 1)-spread of PG(4n− 1, q) and, hence, a translation plane of order q2n. A mixed partition in this case is a partition of the points of PG(2n− 1, q2) into PG(n− 1, q2)’s and PG(2n− 1, q)’s which we call Baer subspaces. In this paper, we completely classify the mixed partitions which generate regular...

In this paper, we give connection between the order of the generalized Baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. Moreover, we give a necessary and sufficient condition in which the generalized Baer-invariant of a pair of groups can be embedded into the generalized Baer-invariant of pair of its factor groups.

In 1954 Zelinsky [16] proved that every element in the ring of linear transformations of a vector space V over a division ring D is a sum of two units unless dim V = 1 and D = Z2. Because EndD(V ) is a (von-Neumann) regular ring, Zelinsky’s result generated quite a bit of interest in regular rings that have the property that every element is a sum of (two) units. Clearly, a ring R, having Z2 as...

We use the concept of a regular object with respect to another object in an arbitrary category, defined in [3], in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R−mod and S−mod, when S is an excellent extension of the ring R. Consequently, we obtain a result of [5]: if S is an excellent extension of the ring R, then S is von Neumann regular ring i...

The BaeSR two-component regulatory system controls expression of exporter genes conferring drug resistance in Escherichia coli (S. Nagakubo, K. Nishino, T. Hirata, and A. Yamaguchi, J. Bacteriol. 184:4161-4167, 2002; N. Baranova and H. Nikaido, J. Bacteriol. 184:4168-4176, 2002). To understand the whole picture of BaeSR regulation, a DNA microarray analysis of the effect of BaeR overproduction ...

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...