A Change of Ring Theorem with Applications to Poincaré Series and Intersection Multiplicity.
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 -module is tensor a bracket group.
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring , denoted by , is a graph with all non-small proper ideals of as vertices and two distinct vertices and are adjacent if and only if is not small in . 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,...