5 papers
A Mayer-Vietoris calculus for regular denominators
Elena Caviglia, Amartya Goswami
Let be a commutative ring and let be an ideal. An element is a regular denominator for when multiplication by on is injective; we denote the set of a…
Detecting Essential Ideals in Polynomial Rings
Amartya Goswami, Luca Mesiti
We characterize essential ideals in polynomial rings over a commutative ring with . We present several characterizations, letting vary among notable c…
Primitive quantales
Amartya Goswami, Elena Caviglia, Luca Mesiti
We generalize Jacobson's notion of primitive ring to the setting of quantales. We show that every primitive ring gives rise to a primitive quantale of ideals. We then prove a densi…
On extensions of Cohen Structure Theorem
Elena Caviglia, Amartya Goswami, Luca Mesiti
The aim of this paper is to extend Cohen structure theorem beyond local rings. Both Cohen structure theorem and Nagata's generalization of it are special cases of our results. We i…
On the Extensions of the Cohen Structure Theorem
Amartya Goswami
The purpose of this note is to pose a question that, when answered, would directly imply the Cohen Structure Theorem. We provide a solution to this question for a specific class of…