Let V = V1 ⊕ V2 be a finite-dimensional vector space over an infinite locally-finite field F . Then V admits the torus action of G = F • by defining (v1 ⊕ v2) = v1g−1 ⊕ v2g. If K is a field of characteristic different from that of F , then G acts on the group algebra K[V ] and it is an interesting problem to determine all G-stable ideals of this algebra. In this paper, we consider the special c...

Let K be a fixed number field, assumed to be Galois over Q. Let r and f be fixed integers with f positive. Given an elliptic curve E , defined over K , we consider the problem of counting the number of degree f prime ideals of K with trace of Frobenius equal to r . Except in the case f = 2, we show that ‘on average,’ the number of such prime ideals with norm less than or equal to x satisfies an...

After traumatic brain injury, extracellular K(+) in brain can dramatically increase. We studied the effects of increased K(+) on the isolated pressurized rat middle cerebral artery (MCA). MCAs (200-250 microm OD) were isolated, cannulated with glass micropipettes, and pressurized. K(+) was increased in the extraluminal bath using three paradigms: (1) isotonic K(+) (K(iso)) where increases in K(...

In recent years, soft sets have become popular in various fields. For this reason, many studies been carried out the field of algebra. study, intersection k-ideals are defined with help a semiring, and some algebraic structures examined. Moreover, quotient rings by k-semiring. Isomorphism theorems examined rings. Finally, properties investigated defining maximal k-ideals.

Let K be a fixed number field, assumed to be Galois over Q. Let r and f be fixed integers with f positive. Given an elliptic curve E, defined over K, we consider the problem of counting the number of degree f prime ideals of K with trace of Frobenius equal to r. Except in the case f = 2, we show that “on average,” the number of such prime ideals with norm less than or equal to x satisfies an as...

We investigate products J of ideals of “row initial” minors in the polynomial ring K [X ] defined by a generic m × n-matrix. The defining “shape” of J determines a set of “row initial” standard bitableaux that we call superstandard. They form a Gröbner basis of J , and J has a linear minimal free resolution. These results are used to derive a new generating set for the Grothendieck group of fin...

1. Let F be a partially ordered vector space with an order unit e. It is well known that the class 5DÎ of maximal ideals of V is in one-one correspondence with the class K of normalized positive linear functionals, in the sense that to each ME^SR corresponds a positive linear functional <¡>m with M as its null-space and with M(e) = 1. A maximal ideal MG 90? is said to be extreme if <pM is an...

In this paper, we introduce a new sort of interval valued $left(in ,in vee q_{widetilde{k}}^{widetilde{delta }}right) $-fuzzy bi-ideal in ordered semigroups which is the generalization of interval valued $left( in ,in vee q_{%widetilde{k}}right) $-fuzzy bi-ideal and interval valued $left( in ,in vee qright) $-fuzzy bi-ideal of ordered semigroups. We give examples in which we show that these str...