this work is devoted to give a charcaterization of a pomonoid $s$such that all cyclic $s$-posets are regular injective.

Preenvelopes of acts over a monoid are defined by analogy with Enochs’ definition preenvelopes modules. Provided that it is closed for pure subacts, class shown to be preenveloping precisely when under direct products. Examples such classes include absolutely pure, weakly f-injective and p-injective acts.

in this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits...

we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

Using only basic topological properties of real algebraic sets and regular morphisms we show that any injective regular self-mapping of a real algebraic set is surjective. Then we show that injective morphisms between germs of real algebraic sets define a partial order on the equivalence classes of these germs divided by continuous semi-algebraic homeomorphisms. We use this observation to deduc...

Although useful in many applications, the medial axis transform (MAT) has a few fit-falls, one of which is its extreme sensitivity to the boundary perturbation. In this paper, we first summarizes the previous attempts to get around this by bounding the one-sided Hausdorff distance of the MAT with respect to the boundary perturbation. We illustrate these results and their optimality with various...