Saeed Nasseh

activity

20072026

most citedLocal rings with quasi-decomposable maximal ideal

42 citations · 56 across the 23 of their papers we have counts for

collaborators

29 papers

math.AC2026

Peskine and Szpiro's Dimension inequality holds over local rings of depth at most one

Lars Winther Christensen, Saeed Nasseh

We prove that the general version---the one that includes the dimension of the tensor product---of Peskine and Szpiro's Dimension Inequality holds over noetherian local rings of de…

math.AC2026

Structure of irreducible homomorphisms to/from free and injective modules

Saeed Nasseh

Let $R$ be a commutative noetherian local ring. We extend the work of the author and Takahashi by investigating the structure of irreducible monomorphisms originating from free mod…

math.AC2026

A counterexample to the localization problem for AB rings

Justin Lyle, Saeed Nasseh

We construct a complete local Gorenstein ring $R$ of dimension $1$ with a prime ideal $p \in Spec (R)$ such that $R$ is an AB ring, but the localization $R_…

math.AC2026

Connections and naïve lifting of DG modules

Saeed Nasseh, Maiko Ono, Yuji Yoshino

In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological al…

math.AC2026

Semi-fiber products of algebras and lifting of complexes

Saeed Nasseh, Maiko Ono, Yuji Yoshino

Let $k$ be a field. In this paper, we define the notion of semi-fiber products of commutative $k$ -algebras and show that the class of such rings contains several classes of commuta…

math.AC2025

Tor algebra of local rings with decomposable maximal ideal

Saeed Nasseh, Maiko Ono, Yuji Yoshino

Let $(R, m_{R})$ be a commutative noetherian local ring. Assuming that $m_{R} =$ $I \oplus J$ is a direct sum decomposition, where $I$ and $J$ are non-zero ideals of $R$ ,…