Some remarks on normal property of graded subalgebras of polynomial rings.
We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.
In this article, we compare different types of representations for series with coefficients in complete idempotent semirings. Each of these representations was introduced to solve a particular problem. We show how they are or are not included one in the other and we present a common generalization of them.
On the ring of polynomials in n variables over a field special isomorphisms ’s of into are defined which preserve the greatest common divisor of two polynomials. The ring is extended to the ring and the ring of generalized polynomials in such a way that the exponents of the variables are non-negative rational numbers and rational numbers, respectively. The isomorphisms ’s are extended to automorphisms ’s of the ring . Using the property that the isomorphisms ’s preserve GCD it...
We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal is a CM Stanley ideal, then is a Stanley ideal as well, where is the polarization of .