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of 72
pro vyhledávání: '"13B21"'
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prime ideals in a Tambara functor. In this work, we continue the study of
Externí odkaz:
http://arxiv.org/abs/2410.23052
Autor:
Secord, Spencer
We present a proof that all straight domains are locally divided$\unicode{x2014}$thereby answering two open problems posed by Dobbs and Picavet, which appeared in the survey "Open Problems in Commutative Ring Theory" written by Cahen, Fontana, Frisch
Externí odkaz:
http://arxiv.org/abs/2305.01809
Autor:
Guerrieri, Lorenzo, Loper, K. Alan
It is well-known that an integrally closed domain $D$ can be express as the intersection of its valuation overrings but, if $D$ is not a Pr\"{u}fer domain, the most of valuation overrings of $D$ cannot be seen as localizations of $D$. The Kronecker f
Externí odkaz:
http://arxiv.org/abs/2304.03723
Autor:
Abrams, Aaron, Pommersheim, Jamie
Publikováno v:
Pacific J. Math. 330 (2024) 199-206
Given a trapezoid dissected into triangles, the area of any triangle determined by either diagonal of the trapezoid is integral over the ring generated by the areas of the triangles in the dissection. Given a parallelogram dissected into triangles, t
Externí odkaz:
http://arxiv.org/abs/2301.03475
Autor:
van der Lee, Matthé
Absolute integral closures of general commutative unital rings are explored. All rings admit absolute integral closures, but in general they are not unique. Among the reduced rings with finitely many minimal prime ideals, finite products of domains a
Externí odkaz:
http://arxiv.org/abs/2212.06738
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomo
Externí odkaz:
http://arxiv.org/abs/1911.02544
Let $R$ be a commutative ring with nonzero identity. A. Yassine et al. defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of $1$-absorbing prime ideals as follows: a proper ideal $I$ of $R$ is said to be a $1$-absorbing prime id
Externí odkaz:
http://arxiv.org/abs/2010.04415
Autor:
Azarang, Alborz
It is shown that if $R$ is a ring, $p$ a prime element of an integral domain $D\leq R$ with $\bigcap_{n=1}^\infty p^nD=0$ and $p\in U(R)$, then $R$ has a conch maximal subring (see \cite{faith}). We prove that either a ring $R$ has a conch maximal su
Externí odkaz:
http://arxiv.org/abs/2009.05995
Autor:
Rangachev, Antoni
Publikováno v:
Journal of Algebra 508 (2018), 301-338
Let $X:=\mathrm{Spec}(R)$ be an affine Noetherian scheme, and $\mathcal{M} \subset \mathcal{N}$ be a pair of finitely generated $R$-modules. Denote their Rees algebras by $\mathcal{R}(\mathcal{M})$ and $\mathcal{R}(\mathcal{N})$. Let $\mathcal{N}^{n}
Externí odkaz:
http://arxiv.org/abs/1611.03910
Autor:
Dumitrescu, Tiberiu, Rani, Anam
We extend to rings with zero-divisors the concept of perinormal domain introduced by N. Epstein and J. Shapiro. A ring $A$ is called perinormal if every overring of $A$ which satisfies going down over $A$ is $A$-flat. The Pr\"ufer rings and the Marot
Externí odkaz:
http://arxiv.org/abs/1609.09216