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pro vyhledávání: '"Shapiro, Jay"'
Autor:
Epstein, Neil, Shapiro, Jay
A ring is *unit-additive* if a sum of units is always either a unit or nilpotent. For example, $k[X]$ and $k[X]/(X^2)$ are unit-additive, but $\mathbb Z$ is not. We prove a wide-ranging theorem about semigroup rings, showing among other things that a
Externí odkaz:
http://arxiv.org/abs/2307.11036
Autor:
Epstein, Neil, Shapiro, Jay
One says that a ring homomorphism $R \rightarrow S$ is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element $f\in S$, there is a unique smallest ideal of $R$ whose extension to $S$ contains $f$, cal
Externí odkaz:
http://arxiv.org/abs/2008.07616
Autor:
Epstein, Neil, Shapiro, Jay
The connection between a univariate polynomial having locally principal content and the content function acting like a homomorphism (the so-called Gaussian property) has been explored by many authors. In this work, we extend several such results to t
Externí odkaz:
http://arxiv.org/abs/1708.02364
Autor:
Epstein, Neil, Shapiro, Jay
The notion of an Ohm-Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan-Hochster proof of Stillman's conjecture. As further restrictions are placed (creating the inc
Externí odkaz:
http://arxiv.org/abs/1703.02114
Autor:
Nicol, Lindsey, Srikanth, Priya, Henriksen, Kim, Sun, Shu, Smith, Rosamund, Karsdal, Morten A., Nagamani, Sandesh C.S., Shapiro, Jay, Lee, Brendan, Leder, Benjamin Z., Orwoll, Eric
Publikováno v:
In Bone January 2021 142
Autor:
Epstein, Neil, Shapiro, Jay
We further develop the notion of perinormality from our last paper, showing that it is preserved by many pullback constructions. In doing so, we introduce the concepts of relative perinormality and fragility for ring extensions.
Comment: Major r
Comment: Major r
Externí odkaz:
http://arxiv.org/abs/1511.06473
Autor:
Epstein, Neil, Shapiro, Jay
Publikováno v:
Journal of Algebra 451 (2016), 65-84
We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give equivalent
Externí odkaz:
http://arxiv.org/abs/1501.03411
Autor:
Epstein, Neil, Shapiro, Jay
Publikováno v:
J. Algebra Appl. 15 (2016), no. 1, 1650009, 14 pp
The content of a polynomial over a ring $R$ is a well understood notion. Ohm and Rush generalized this concept of a content map to an arbitrary ring extension of $R$, although it can behave quite badly. We examine five properties an algebra may have
Externí odkaz:
http://arxiv.org/abs/1405.3000
Autor:
Epstein, Neil, Shapiro, Jay
We prove a power series ring analogue of the Dedekind-Mertens lemma. Along the way, we give limiting counterexamples, we note an application to integrality, and we correct an error in the literature.
Comment: Added two references, as per referee
Comment: Added two references, as per referee
Externí odkaz:
http://arxiv.org/abs/1402.1100
Autor:
Epstein, Neil, Shapiro, Jay
Publikováno v:
J. Pure Appl. Algebra 218 (2014), no. 9, 1712-1729
There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable replacemen
Externí odkaz:
http://arxiv.org/abs/1303.7458