On commutative principal ideal semigroup rings.
On commutative rings whose maximal ideals are idempotent
We prove that for a commutative ring , every noetherian (artinian) -module is quasi-injective if and only if every noetherian (artinian) -module is quasi-projective if and only if the class of noetherian (artinian) -modules is socle-fine if and only if the class of noetherian (artinian) -modules is radical-fine if and only if every maximal ideal of is idempotent.
On commutative rings whose prime ideals are direct sums of cyclics
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring , the following statements are equivalent: (1) Every prime ideal of is a direct sum of cyclic -modules; (2) where is an index set and is a principal ideal ring for each ; (3) Every prime ideal of is a direct sum of at most...
On Commutative Semigroups of Polynomials with Respect to Composition.
On composition of formal power series.
On constructing resolutions over the polynomial algebras.
On constructivizability of the tensor product of modules.
On coverings of almost Dedekind domains
On c-semigroups
On curves on rational normal scrolls.
On Dedekind domains in infinite algebraic extensions
On Dedekind's criterion and monogenicity over Dedekind rings.
On deformation method in invariant theory
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let be a reductive group, an affine -variety and a spherical subgroup. We show that whenever is affine and its semigroup of weights is saturated, the algebra of -invariant regular functions on has a -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of . The deformation method in its usual form, as developed...
On deformations of pasting diagrams.
On delta sets and their realizable subsets in Krull monoids with cyclic class groups
Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question of determining...
On differential rational invariants of finite subgroups of affine group.
On domains with ACC on invertible ideals
If is a domain with the ascending chain condition on (integral) invertible ideals, then the group of its invertible ideals is generated by the set of maximal invertible ideals. In this note we study some properties of and we prove that, if is a free group on , then is a locally factorial Krull domain.
On efficient generation of ideals.
On endomorphism algebras over admissible Dedekind domains
On endomorphisms of multiplication and comultiplication modules
Let be a ring with an identity (not necessarily commutative) and let be a left -module. This paper deals with multiplication and comultiplication left -modules having right -module structures.