Arbitrarily large indecomposable divisible torsion modules over certain valuation domains
Archimedean frames, revisited
This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called joinfitness and is Choice-free. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an infinitesimal element arises naturally,...
Arithmetic euclidean rings
Arithmetic functions over rings with zero divisors.
Arithmetic of block monoids
Arithmetic of non-principal orders in algebraic number fields
Let be an order in an algebraic number field. If is a principal order, then many explicit results on its arithmetic are available. Among others, is half-factorial if and only if the class group of has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.
Arithmetic on two dimensional local rings.
Arithmetic progressions in a unique factorization domain
Arithmetical aspects of saturation of singularities
Arithmetical properties of finite rings and algebras, and analytic number theory. III. Finite modules and algebras over Dedekind domains.
Arithmetical quadratic surfaces of genus 0, II.
Arithmetical theory of monoid homomorphisms.
Arithmetically Cohen-Macaulay curves in P4 of degree 4 and genus 0.
Aritmética de los semigrupos de Arf y saturados. Aplicaciones.
Artin Approximation and Formal Fibres of Local Rings.
Artinian cofinite modules over complete Noetherian local rings
Let be a complete Noetherian local ring, an ideal of and a nonzero Artinian -module. In this paper it is shown that if is a prime ideal of such that and is not finitely generated and for each the -module is of finite length, then the -module is not of finite length. Using this result, it is shown that for all finitely generated -modules with and for all integers , the -modules are of finite length, if and only if, for all finitely generated -modules with and...
Artinian modules are countably generated
Artinianness of formal local cohomology modules
Let be an ideal of Noetherian local ring and a finitely generated -module of dimension . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to . Also we prove that for an arbitrary local ring (not necessarily complete), we have
Artin-Nagata properties and Cohen-Macaulay associated graded rings
Artin's conjecture on primes with prescribed primitive roots