A General Theory of Relative Regular Neighborhoods

Ranks of modules relative to a torsion theory

Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...

Regular Neighborhoods Are Not Topologically Invariant

Non-regular |2|-graded geometries I: general theory

This paper analyses non-regular |2|-graded geometries, and show that they share many of the properties of regular geometries – the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as obstruction to flatness of the geometry, the existence of the first two BGG splitting operators and of (in most cases) invariant prolongations for the standard Tractor b...

Codimension Two Pl Embeddings of Spheres with Nonstandard Regular Neighborhoods

Abstract. For a given polyhedron K ⊂ M the notation RM (K) denotes a regular neighborhood of K in M . We study the following problem: find all pairs (m,k) such that if K is a compact k-polyhedron and M a PL m-manifold, then RM (fK) ∼= RM (gK), for each two homotopic PL embeddings f, g : K → M . We prove that R Sk+2 (S) 6∼= S × D for each k ≥ 2 and some PL sphere S ⊂ S (even for any PL sphere S ...

applying transitivity theory to gender analysis of efl textbook: : a comparative study.

efl/esl textbooks have been regarded as essential language teaching materials with which the learners spend about 70 up to 90 percent of their class time. the important role they play and their vast use make them not only influential in learning the language but also in shaping values and attitudes. put it another way, textbooks socialize learners using their contents (i.e. texts, illustrations...