243 research outputs found

    Ascent and descent of the Golod property along algebra retracts

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    We study ascent and descent of the Golod property along an algebra retract. We characterise trivial extensions of modules, fibre products of rings to be Golod rings. We present a criterion for a graded module over a graded affine algebra of characteristic zero to be a Golod module.Comment: 16 page

    Non-conservation of Density of States in Bi2_2Sr2_2CaCu2_2Oy_y: Coexistence of Pseudogap and Superconducting gap

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    The tunneling spectra obtained within the ab-plane of Bi2_2Sr2_2CaCu2_2Oy_y (Bi2212) for temperatures below and above the critical temperature (Tc_c) are analyzed. We find that the tunneling conductance spectra for the underdoped compound in the superconducting state do not follow the conservation of states rule. There is a consistent loss of states for the underdoped BI2212 implying an underlying depression in the density of states (DOS) and hence the pseudogap near the Fermi energy (EF_F). Such an underlying depression can also explain the peak-dip-hump structure observed in the spectra. Furthermore, the conservation of states is recovered and the dip-hump structure disappears after normalizing the low temperature spectra with that of the normal state. We argue that this is a direct evidence for the coexistence of a pseudogap with the superconducting gap.Comment: 5 pages, 4 figure

    On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings

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    Let RR be a commutative ring of dimension dd, S=R[X]S = R[X] or R[X,1/X]R[X, 1/X] and PP a finitely generated projective SS module of rank rr. Then PP is cancellative if PP has a unimodular element and rd+1r \geq d + 1. Moreover if rdim(S)r \geq \dim (S) then PP has a unimodular element and therefore PP is cancellative. As an application we have proved that if RR is a ring of dimension dd of finite type over a Pr\"{u}fer domain and PP is a projective R[X]R[X] or R[X,1/X]R[X, 1/X] module of rank at least d+1d + 1, then PP has a unimodular element and is cancellative.Comment: 21 page

    Characterizations of regular local rings via syzygy modules of the residue field

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    Let RR be a commutative Noetherian local ring with residue field kk. We show that if a finite direct sum of syzygy modules of kk surjects onto `a semidualizing module' or `a non-zero maximal Cohen-Macaulay module of finite injective dimension', then RR is regular. We also prove that RR is regular if and only if some syzygy module of kk has a non-zero direct summand of finite injective dimension.Comment: 7 page
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