The multiplicative closed set Sa

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Z be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Z such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Z is an affine variety over an algebraically closed field.

Multiplicative Complexity of Commutative Group Algebras over Algebraically Closed Fields

We determine structure and multiplicative complexity of commutative group algebras over algebraically closed fields. Commutative group algebra A of dimension n over algebraically closed field is isomorphic to B, where B is a superbasic algebra of minimal rank (see [5] for definition), and t is maximal that t | n, p t. Multiplicative and bilinear complexity of A equal to 2n − t.

Algebraically Closed Fields with a Generic Multiplicative Character

We study the model theory of the 2-sorted structure (F,C;χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. We obtain an axiomatization ACFCp of Th(F,C;χ) in a suitable language L, classify the models of ACFCp up to isomorphism, prove a modified model companion result, give va...

characterizing the multiplicative group of a real closed field in terms of its divisible maximal subgroup