Note on the transitivity of pure essential extensions
Note sur la méthode d'élimination de Bezout
Notes on annihilator conditions in modules over commutative rings.
Notes on generalizations of Bézout rings
In this paper, we give new characterizations of the --Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non--Bézout --Bézout rings and examples of non--Bézout --Bézout rings.
Notes on structure of complete discrete valuation rings.
On a functional equation arising from hyperbolic geometry.
On a generalization of a Prüfer-Kaplansky-Procházka theorem
On -Kasch spaces
If is a Tychonoff space, its ring of real-valued continuous functions. In this paper, we study non-essential ideals in . Let be a infinite cardinal, then is called -Kasch (resp. -Kasch) space if given any ideal (resp. -ideal) with then is a non-essential ideal. We show that is an -Kasch space if and only if is an almost -space and is an -Kasch space if and only if is a pseudocompact and almost -space. Let denote the socle of . For a topological space with only...
On a Retract of an Integral Domain.
On a theorem of F. S. Macaulay on colon ideals.
On almost discrete space
Let be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of . The intersection of essential weak ideal in is also studied.
On Armendariz rings.
On associated and attached prime ideals of certain modules
Primary and secondary functors have been introduced in [2] and applied to extend some results concerning asymptotic prime ideals. In this paper, the theory of primary and secondary functors is developed and examples of non-exact primary and non-exact secondary functors are presented. Also, as an application, the sets of associated and of attached prime ideals of certain modules are determined.
On chains of centered valuations.
On chains of free modules over valuation domains
On Cohen's theorem
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 coverings of almost Dedekind domains
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 differential rational invariants of finite subgroups of affine group.