If z has order q* and n is of the form n =m+q, then either k= m(q*+q+ l), or k= (m+q)(q*-q+ 1). Obviously, in case m=O, K is a maximal arc. Moreover, if m = 1 and q is a prime power, then K is either a Baer subplane or a unital [lo]. Furthermore, m pairwise disjoint Baer subplanes of n always yield a set of type (m, m + q) and size m(q* + q + 1). In case rc is Desarguesian, such a set does exis...

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer ∗semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer ∗-semigroups.

Mutant 7F2 of Salmonella enterica serovar Typhimurium has a transposon inserted in the regulator gene baeR of a two-component system and showed a more-than-fourfold reduction in resistance to ceftriaxone. Complementation analysis suggested an association among the outer membrane proteins OmpW and STM3031, ceftriaxone resistance, and baeR.

Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...