Rigid Ideals in Gorenstein Rings of Dimension One
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DOI: 10.1007/s40306-018-00315-0
Abstract: Motivated by a conjecture of Huneke and Wiegand concerning torsion in tensor products of modules over local rings, we investigate the existence of ideals I in a one-dimensional Gorenstein local ring R satisfying ExtR1(I,I)=0$\text {Ext}^{1}_{R}(I,I)= 0$. read more here.
Keywords: rigid ideals; dimension one; rings dimension; ideals gorenstein ... See more keywords
Sally modules of canonical ideals in dimension one and 2-AGL rings
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DOI: 10.1016/j.jalgebra.2018.11.023
Abstract: The notion of 2-AGL ring in dimension one which is a natural generalization of almost Gorenstein local ring is posed in terms of the rank of Sally modules of canonical ideals. The basic theory is… read more here.
Keywords: dimension one; one agl; ideals dimension; sally modules ... See more keywords
The three-body problem in dimension one: From short-range to contact interactions
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DOI: 10.1063/1.5030170
Abstract: We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such Hamiltonian converges to… read more here.
Keywords: dimension one; varepsilon sigma; sigma; short range ... See more keywords
On finiteness of prime cones over simple ADE-singularities of dimension one
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DOI: 10.1080/00927872.2018.1430808
Abstract: ABSTRACT A local ring is called a local ring of simple singularity of dimension one over the real field if it is isomorphic to a ring of the form ℝ{x,y}∕(f) and the number of proper… read more here.
Keywords: dimension one; ade singularities; prime cones; finiteness prime ... See more keywords
Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one
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DOI: 10.1088/1361-6544/ab1273
Abstract: The paper discusses nonlinear singular perturbations of delta type of the fractional Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, with $s\in(\frac{1}{2},1]$, in dimension one. Precisely, we investigate local and global well posedness (in a strong sense), conservations laws and… read more here.
Keywords: singular perturbations; nonlinear singular; dimension one; fractional schr ... See more keywords