It was conjectured by White in 1980 that the toric ring associated to a matroid is defined symmetric exchange relations. This conjecture extended discrete polymatroids Herzog and Hibi, they prove holds for with so called strong property. In this paper we generalize their result are products of also extends Conca on transversal polymatroids.

We construct an example of a quasi-o-minimal group without the Exchange Property. A structure hM;<;:::i is called quasi-o-minimal 1] if in any structure elementarily equivalent to it the deenable subsets are exactly the Boolean combinations of 0-deenable subsets and intervals. A complete theory T is said to have the Exchange Property if, for any model M of T and for any X M and b; c 2 M, if b 2...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

Nonsteroidal anti-inflamatory drugs (NSAIDs) and glucocorticoids, nowaday are the main groups of anti-inflamatory drugs in modern pharmacology. The side effects of these antiinflamatory drugs, specially using in chronic diseases cause many problems for the patients and the physicians, so finding the new anti-inflamatory drugs with less side effect is the aim of many researchers. WHO emphasiz to...

Nonsteroidal anti-inflamatory drugs (NSAIDs) and glucocorticoids, nowaday are the main groups of anti-inflamatory drugs in modern pharmacology. The side effects of these antiinflamatory drugs, specially using in chronic diseases cause many problems for the patients and the physicians, so finding the new anti-inflamatory drugs with less side effect is the aim of many researchers. WHO emphasiz to...