Saeed Nasseh

collaborators

4 papers

math.AC2026

Connections and naÃ¯ve 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 $R$ ,…

math.AC2025

Vector space summands of lower syzygies

Mohsen Asgharzadeh, Michael DeBellevue, Souvik Dey +2

In this paper, we investigate problems concerning when the residue field $k$ of a local ring $(R, m$ , $k)$ appears as a direct summand of syzygy modules, from two perspectives…