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Some remarks on Prüfer modules

S. Ebrahimi Atani, S. Dolati Pishhesari, M. Khoramdel (2013)

Discussiones Mathematicae - General Algebra and Applications

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}.

Special isomorphisms of F [ x 1 , ... , x n ] preserving GCD and their use

Ladislav Skula (2009)

Czechoslovak Mathematical Journal

On the ring R = F [ x 1 , , x n ] of polynomials in n variables over a field F special isomorphisms A ’s of R into R are defined which preserve the greatest common divisor of two polynomials. The ring R is extended to the ring S = F [ [ x 1 , , x n ] ] + and the ring T = F [ [ x 1 , , x n ] ] of generalized polynomials in such a way that the exponents of the variables are non-negative rational numbers and rational numbers, respectively. The isomorphisms A ’s are extended to automorphisms B ’s of the ring S . Using the property that the isomorphisms A ’s preserve GCD it...

Stanley decompositions and polarization

Sarfraz Ahmad (2011)

Czechoslovak Mathematical Journal

We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal I is a CM Stanley ideal, then I p is a Stanley ideal as well, where I p is the polarization of I .

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