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In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ 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 $(R, ℳ)$ , the following statements are equivalent: (1) Every prime ideal of $R$ is a direct sum of cyclic $R$ -modules; (2) $ℳ = ⨁_{λ \in Λ} R w_{λ}$ where $Λ$ is an index set and $R / Ann (w_{λ})$ is a principal ideal ring for each $λ \in Λ$ ; (3) Every prime ideal of $R$ is a direct sum of at most...

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La théorie des anneaux japonais

Large homomorphisms of local rings.

Localisation de formes quadratiques $I$

Localisation de formes quadratiques. II

Majoration des caractéristiques d'Euler-Poincaré partielles

Minimal injective resolutions

Modulo canonico di anelli ridotti di dimensione uno e semigruppi loro associati. t-successioni

Nagata's Criterion and Openness of Loci for Gorenstein and Complete Intersection.

Normal and tangential flatness.

Note on Asymptotic Prime Divisors and Symbolic Powers of Primary Ideals.

On Castelnuovo's regularity and Hilbert functions

On commutative rings whose prime ideals are direct sums of cyclics

On h-regular graded algebras

On prime divisors of the integral closure of a principal ideal.

On some algebraic and geometric extension of the theory of adjoints

On some results of L. J. Ratliff

On the branches of a complex space.

On the Prime Ideal of an Ordering of Higher Level.

On the structure of non-excellent curve singularities in characteristic $p$

On the upper semicontinuity intersection defect.

Currently displaying 41 – 60 of 105