In the ideal topological spaces (X, ?, I) and (Y, J, ?), we define (I, J)-irresolute function, weakly-(I, J)-irresolute, strongly-(I, functions, semi-I-open sets quasi-H-closed modulo I. We discuss properties of function mapping connected, closed, compact I semi-I-isolated points. J)-Homeomorphisim on presemi-I-open closure subsets are explored in this paper.

We study tight closure and test ideals in rings of characteristic p 0 using resolution of singularities. The notions of F -rational and F regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the test ideal, and generalize it to wider cl...

In this article we investigate homological aspects of a skew complete intersection R, i.e. polynomial ring modulo an ideal generated by sequence regular normal elements. We compute the derived braided Hochschild cohomology R relative to and show its action on ExtR(M,N) is noetherian for finitely R-modules M N respecting braiding R. When parameters defining are roots unity use define support the...

We define and study the Milnor K-ring of a field F modulo a subgroup of the multiplicative group of F . We compute it in several arithmetical situations, and study the reflection of orderings and valuations in this ring. Introduction Let F be a field and let F× be its multiplicative group. The Milnor K-ring K ∗ (F ) of F is the tensor (graded) algebra of the Z-module F× modulo the homogenous id...

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis...

Factorization algorithms over Q[X] and Fp[X] are key tools of computational number theory. Many algorithms over number fields rely on the possibility of factoring polynomials in those fields. Because of the recent development of relative methods in computational number theory, see for example (Cohen et al. 1998, Daberkow and Pohst 1995), efficient generalizations of factorization algorithms to ...

For a graph G, we construct two algebras whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis ...

We generalist Gabidulin codes to the case of infinite fields, eventually with characteristic zero. For this purpose, we consider an abstract field extension and any automorphism in the Galois group. We derive some conditions on the automorphism to be able to have a proper notion of rank metric which is in coherence with linearized polynomials. Under these conditions, we generalize Gabidulin cod...