A regular parallelism of real projective 3-space PG(3,R) is an equivalence relation on the line space such that every class equivalent to set 1-dimensional complex subspaces a 2-dimensional vector space. We shall assume classes compact, and characterize those parallelisms admit action torus group. prove there one-dimensional subtorus fixing parallel class. From this property alone we deduce 2- ...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

Three machine implemented algorithms for computing with integral orders are described. The algorithms are: 1. For an integral order R given in terms of its left regular representation relative to any basis, compute the nil radical J(R) and a left regular representation of R/J(R). 2. For a semisimple order R given in terms of its left regular representation relative to any basis, compute a new b...

We characterize strong F-regularity, a property associated with tight closure, in a large class of rings. A special case of our results is a workable criterion in complete intersection rings. Tight closure is a recently introduced operation linked to a variety of results in commutative algebra. Among the major results achieved with its use are a generalization of the Direct Summand Conjecture f...

the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green's relations $mbox{$...

This paper discusses a learning algorithm for regular sets in the model of learning in the limit from complete data (i.e., positive and negative data). We rst present some characterization results for regular sets in the rough set theoretic framework. More speci cally, it is shown that any regular set is R-de nable for some kinds of equivalence relations R of nite index. We then show that regul...

For every prime integer p, M. Hochster conjectured the existence of certain p-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prim...

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...