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.

Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a cer...

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...

Throughout this paper, all groups are finite. A group class closed under taking homomorphic images and finite subdirect products is called a formation . The symbol σ denotes some partition of the set primes. V. G. Safonov, I. N. Safonova, A. Skiba (Commun. Algebra. 2020. Vol. 48, № 9. P. 4002–4012) defined generalized σ-function. Any function f form : È {Ø} → {formations groups}, where (Ø) ≠ ∅,...