Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the violation of the refined planar stability condition of Zumbrun–Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we ...

Let R be a commutative noetherian ring and let $$\mathfrak {a}$$ an ideal of R. In this paper, we study certain condition, namely $$C_{\mathfrak {a}}$$ , introduced by Aghapournahr Melkersson, on the extension two subcategories R-modules. We develop some main results Yoshizawa (Proc Am Math Soc 140(7):2293–2305, 2012; J Commut Algebra 13:137–155, 2021). As example subcategories, weakly Laskeria...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

Let [Formula: see text] be an text]-finite, Krull–Schmidt and text]-linear text]-exangulated category with a commutative artinian ring. In this note, we prove that has Auslander–Reiten–Serre duality if only Auslander–Reiten text]-exangles. Moreover, also give equivalent condition for the existence of Serre (which is special type duality). Finally, assume further duality. We exploit bijection tr...

1. Yang-Baxter algebras (YBA), introduced in [1, 2, 3], generalize the wideknown FRT construction [4] in the following sense: to any numerical matrix solution R of the Yang-Baxter equation there is associated a bialgebra containing the FRT one as a sub-bialgebra. Generally, this construction may provide examples of (new) bialgebras and Hopf algebras [5]. In several aspects, there is some simila...

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

We prove a general criterion which ensures that fractional Calabi--Yau category of dimension $\leq 2$ admits unique Serre-invariant stability condition, up to the action universal cover $\text{GL}^+_2(\mathbb{R})$. apply this result Kuznetsov component $\text{Ku}(X)$ cubic threefold $X$. In particular, we show all known conditions on are invariant with respect Serre functor and thus lie in same...

We extend the theory of generalized divisors so as to work on any scheme X satisfying the condition S2 of Serre. We define a generalized notion of Gorenstein biliaison for schemes in projective space. With this we give a new proof of the theorem of Gaeta, that standard determinantal schemes are in the Gorenstein biliaison class of a complete intersection.

We establish bounds for the coefficient e1(I) of the Hilbert function of the integral closure filtration of equimultiple ideals. These values are shown to help control all algorithmic processes of normalization that make use of extensions satisfying the condition S2 of Serre.