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A class of torsion-free abelian groups characterized by the ranks of their socles

Ulrich F. Albrecht, Anthony Giovannitti, H. Pat Goeters (2002)

Czechoslovak Mathematical Journal

Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket R -module is R tensor a bracket group.

A generalization of semiflows on monomials

Hamid Kulosman, Alica Miller (2012)

Mathematica Bohemica

Let K be a field, A = K [ X 1 , , X n ] and 𝕄 the set of monomials of A . It is well known that the set of monomial ideals of A is in a bijective correspondence with the set of all subsemiflows of the 𝕄 -semiflow 𝕄 . We generalize this to the case of term ideals of A = R [ X 1 , , X n ] , where R is a commutative Noetherian ring. A term ideal of A is an ideal of A generated by a family of terms c X 1 μ 1 X n μ n , where c R and μ 1 , , μ n are integers 0 .

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

Sarti, Alessandra (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.

A graph associated to proper non-small ideals of a commutative ring

S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring R , denoted by G ( R ) , is a graph with all non-small proper ideals of R as vertices and two distinct vertices I and J are adjacent if and only if I J is not small in R . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...

A minimal Set of Generators for the Ring of multisymmetric Functions

David Rydh (2007)

Annales de l’institut Fourier

The purpose of this article is to give, for any (commutative) ring A , an explicit minimal set of generators for the ring of multisymmetric functions T S A d ( A [ x 1 , , x r ] ) = A [ x 1 , , x r ] A d 𝔖 d as an A -algebra. In characteristic zero, i.e. when A is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...

A nonlinearizable action of S 3 on 4

Gene Freudenburg, Lucy Moser-Jauslin (2002)

Annales de l’institut Fourier

The main purpose of this article is to give an explicit algebraic action of the group S 3 of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.

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