Finding roots of nonlinear systems of equations on a domain.
Finite and infinite collections of multiplication modules.
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Finite bases for integral closures.
Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring.
Finite cyclic groups and the k-HFD property
Finite dimensional completions in Noether lattices
Finite dimensional rings of quotients.
In this paper we characterize commutative rings with finite dimensional classical ring of quotients. To illustrate the diversity of behavior of these rings we examine the case of local rings and FPF rings. Our results extend earlier work on rings with zero-dimensional rings of quotients.
Finite generating system of matrix invariants.
Finite mutation classes of coloured quivers
We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.
Finite Polynomial Orbits in Finitely Generated Domains.
Finite Separable Field Extensions With Prescribed Extensions of Valuations. II
Finite simplicial multicomplexes.
Finitely generated Ext algebras.
Finitely generated projective ideals in commutative rings.
Finitely generated projective modules and Fitting ideals.
Finiteness aspects of Gorenstein homological dimensions
We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R),...
Finiteness of local homology modules
Let be an ideal of Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let , we will prove that for any integer
Finiteness properties of local cohomology modules (an application of D-modules to Commutative Algebra).
Finiteness results for Abelian tree models
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure....