Universal solvability of group equations

Solvability of Equations in Varieties of Universal Algebras

We study classes of universal algebras in a variety that are closed under the formation of Cartesian products, homomorphic images and extensions. We prove a Birkhoff type theorem for such axiomatic classes. Let V be a variety of algebras of a fixed type τ and let S be a set of first order sentences in the language of τ of the form (∃x1) . . . (∃xn)((u1 = v1) ∧ · · · ∧ (um = vm)), where u1, v1, ...

Group Solvability

Solvability of Diophantine Equations

Attila Bérczes (University of Debrecen): On arithmetic properties of solutions of norm form equations. Abstract. Let α be an algebraic number of degree n and K := Q(α). Consider the norm form equation NK/Q(x0 + x1α+ x2α + . . .+ xn−1α) = b in x0, . . . , xn−1 ∈ Z. (1) Let H denote the solution set of (1). Arranging the elements of H in an |H| × n array H, one may ask at least two natural questi...

Solvability of Systems of Linear Operator Equations

Let G be a semigroup of commuting linear operators on a linear space S with the group operation of composition. The solvability of the system of equations /,/ = ,■, i = I, ... , r, where /, e G and j e S , was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions Ijfr = Irfj , i ^ j , are necessar...

Solvability of Systems of Linear Interval Equations