In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

Let K be the number field determined by a monic irreducible polynomial f(x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f(x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these constructive representations of the prime ideals...

We investigate the ideal structures of the C∗-algebras arising from topological graphs. We give the complete description of ideals of such C∗-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C∗algebras to be simple, prime or primitive. We completely deter...

We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

We generalize the concept of fuzzy point, intutionistic fuzzy point, cubic point by introducing the concept of neutrosophic cubic point. Based on neutrosophic cubic point we generalized the idea of ( ; )-fuzzy ideals, ( ; )-intutionistic fuzzy ideals, ( ; )-cubic ideals ideals by initiating the new concept of neutrosophic Cubic ( ; )-ideals. Particularly we give the idea of neutrosophic cubic (...

We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.

We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This ...