Let A be a commutative R–algebra of finite transcendence degree d ∈ N. We investigate the relationship between the subring of (geometrically) bounded elements H(A) := {a ∈ A | ∃ν ∈ N : |a| ≤ ν on SperA} and the subring of arithmetically bounded elements H (A) := {a ∈ A | ∃ν ∈ N : ν + a and ν − a are sums of squares in A}. Obviously, H ′(A) ⊆ H(A). In 1991, Schmüdgen proved the remarkable theore...

We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...

It is shown that any finitely generated subring of a global field has universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring integers and subsequent extensions to rings number fields $S$-integers function odd characteristic. In this article proof presented which uniform all fields, including characteristic two case, where entirely novel. Furthermor...

Suppose D is an integral domain with quotient eld K and that L is an extension eld of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by All rings considered in this paper are assumed to...

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper. In this note we answer a question by Todorov and Vernaeve (see, e.g., [35]) concerning the relationship between the field of logarithmic-exponential series from [14] and the...

The ever increasing demand for interconnect bandwidth in embedded parallel processors has motivated the development of photonic communications technologies that effectively support short-distance links. Electrooptical I/O to and from VLSI chips is one such photonic technology. A multiring architecture that exploits optical I/O on and off chip is described in [1]. At the heart of the system is a...

Let S be an unramified regular local ring of mixed characteristic two and R the integral closure in a biquadratic extension its quotient field obtained by adjoining roots sufficiently general square free elements f,g?S. S2 denote subring lifting to image Frobenius map on S/2S. When at least one f,g?S2, we characterize Cohen-Macaulayness show that admits birational small Cohen-Macaulay module. I...