243 research outputs found
Ascent and descent of the Golod property along algebra retracts
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 BiSrCaCuO: Coexistence of Pseudogap and Superconducting gap
The tunneling spectra obtained within the ab-plane of
BiSrCaCuO (Bi2212) for temperatures below and above the
critical temperature (T) 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 (E).
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
Let be a commutative ring of dimension , or and
a finitely generated projective module of rank . Then is
cancellative if has a unimodular element and . Moreover if then has a unimodular element and therefore is
cancellative. As an application we have proved that if is a ring of
dimension of finite type over a Pr\"{u}fer domain and is a projective
or module of rank at least , then has a
unimodular element and is cancellative.Comment: 21 page
Characterizations of regular local rings via syzygy modules of the residue field
Let be a commutative Noetherian local ring with residue field . We
show that if a finite direct sum of syzygy modules of surjects onto `a
semidualizing module' or `a non-zero maximal Cohen-Macaulay module of finite
injective dimension', then is regular. We also prove that is regular if
and only if some syzygy module of has a non-zero direct summand of finite
injective dimension.Comment: 7 page
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