This article treats the problem of deriving the reflector of a semi-abelian category A onto a Birkhoff subcategory B of A. Basing ourselves on Carrasco, Cegarra and Grandjeán’s homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization—to semi-abelian categories— of Barr and Beck’s cotriple homology theory. This results in a semi-a...

This article continues the study of multiple blocking sets in PG(2, q). In [3], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t < q1/4/2, of size smaller than t(q + 1) + cqq 2/3, with cq = 2 −1/3 when q is a power of 2 or 3 and cq = 1 otherwise, contain the union of t pairwise disjoint Baer subplanes when t ≥ 2, or a line or a Baer subplane when t = ...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...

Let R be a ring with identity, M right R-module and F fully invariant submodule of M. The concept an F-inverse split module has been investigated recently. In this paper, we approach to different perspective, that is, deal notion F-image M, study various properties obtain some characterizations kind modules. By means modules focus on in which submodules are dual Rickart direct summands. way, co...

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

Existing bounds on the minimum weight d of the dual 7-ary code of a projective plane of order 49 show that this must be in the range of 75 < d < 99. We use combinatorial arguments to improve this range to 87 < d < 99, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case. A brief survey of known results for the minimum weight of the dual...

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...