Search results for "Associated prime"
showing 2 items of 2 documents
Prime Rings Whose Units Satisfy a Group Identity. II
2003
Abstract Let R be a prime ring and 𝒰(R) its group of units. We prove that if 𝒰(R) satisfies a group identity and 𝒰(R) generates R,then either R is a domain or R is isomorphic to the algebra of n × n matrices over a finite field of order d. Moreover the integers n and d depend only on the group identity satisfed by 𝒰(R). This result has been recently proved by C. H. Liu and T. K. Lee (Liu,C. H.; Lee,T. K. Group identities and prime rings generated by units. Comm. Algebra (to appear)) and here we present a new different proof.
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…