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arXiv · 2601.05517

Semi-fiber products of algebras and lifting of complexes

Saeed Nasseh·Maiko Ono·Yuji Yoshino
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Abstract

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 commutative rings, including that of the fiber products of local $k$-algebras over their common residue field $k$. For a noetherian local $k$-algebra $R$ and an ideal $I$ of $R$, under certain conditions, we characterize the liftability of $k$ along the natural surjection $R\twoheadrightarrow R/I$ in terms of retractions, sections, and the existence of semi-fiber product decompositions of $R$.

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Saeed Nasseh, Maiko Ono, Yuji Yoshino. 2026-01-09. Semi-fiber products of algebras and lifting of complexes. https://arxiv.org/abs/2601.05517

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