154 research outputs found
A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS
It was shown by Bergman that the Jacobson radical of a Z-graded ring is
homogeneous. This paper shows that the analogous result holds for nil rings,
namely, that the nil radical of a Z-graded ring is homogeneous.
It is obvious that a subring of a nil ring is nil, but generally a subring of
a Jacobson radical ring need not be a Jacobson radical ring. In this paper it
is shown that every subring which is generated by homogeneous elements in a
graded Jacobson radical ring is always a Jacobson radical ring. It is also
observed that a ring whose all subrings are Jacobson radical rings is nil. Some
new results on graded-nil rings are also obtained
On lattices, modules and groups with many uniform elements
The uniform dimension, also known as Goldie
dimension, can be defined and used not only in the class of modules,
but also in large classes of lattices and groups. For considering this
dimension it is necessary to involve uniform elements.
In this paper we are going to discuss properties of lattices with
many uniform elements. Further, we examine these properties in
the case of lattices of submodules and of subgroups. We also formulate some questions related to the subject of this note
Spin-orbit density wave induced hidden topological order in URu2Si2
The conventional order parameters in quantum matters are often characterized
by 'spontaneous' broken symmetries. However, sometimes the broken symmetries
may blend with the invariant symmetries to lead to mysterious emergent phases.
The heavy fermion metal URu2Si2 is one such example, where the order parameter
responsible for a second-order phase transition at Th = 17.5 K has remained a
long-standing mystery. Here we propose via ab-initio calculation and effective
model that a novel spin-orbit density wave in the f-states is responsible for
the hidden-order phase in URu2Si2. The staggered spin-orbit order 'spontaneous'
breaks rotational, and translational symmetries while time-reversal symmetry
remains intact. Thus it is immune to pressure, but can be destroyed by magnetic
field even at T = 0 K, that means at a quantum critical point. We compute
topological index of the order parameter to show that the hidden order is
topologically invariant. Finally, some verifiable predictions are presented.Comment: (v2) Substantially modified from v1, more calculation and comparison
with experiments are include
Enhanced spin-phonon-electronic coupling in a 5d oxide
Enhanced coupling of material properties offers new fundamental insights and routes to multifunctional devices. In this context 5d oxides provide new paradigms of cooperative interactions that drive novel emergent behaviour. This is exemplified in osmates that host metal-insulator transitions where magnetic order appears intimately entwined. Here we consider such a material, the 5d perovskite NaOsO3, and observe a coupling between spin and phonon manifested in a frequency shift of 40 cm(-1), the largest measured in any material. The anomalous modes are shown to involve solely Os-O interactions and magnetism is revealed as the driving microscopic mechanism for the phonon renormalization. The magnitude of the coupling in NaOsO3 is primarily due to a property common to all 5d materials: the large spatial extent of the ion. This allows magnetism to couple to phonons on an unprecedented scale and in general offers multiple new routes to enhanced coupled phenomena in 5d materials.open0
Coexistence of metallic and nonmetallic properties in the pyrochlore Lu2Rh2O7
Transition metal oxides of the and block have recently become the
targets of materials discovery, largely due to their strong spin-orbit coupling
that can generate exotic magnetic and electronic states. Here we report the
high pressure synthesis of LuRhO, a new cubic pyrochlore oxide
based on Rh and characterizations via thermodynamic, electrical
transport, and muon spin relaxation measurements. Magnetic susceptibility
measurements reveal a large temperature-independent Pauli paramagnetic
contribution, while heat capacity shows an enhanced Sommerfeld coefficient,
= 21.8(1) mJ/mol-Rh K. Muon spin relaxation measurements confirm
that LuRhO remains paramagnetic down to 2 K. Taken in combination,
these three measurements suggest that LuRhO is a correlated
paramagnetic metal with a Wilson ratio of . However, electric
transport measurements present a striking contradiction as the resistivity of
LuRhO is observed to monotonically increase with decreasing
temperature, indicative of a nonmetallic state. Furthermore, although the
magnitude of the resistivity is that of a semiconductor, the temperature
dependence does not obey any conventional form. Thus, we propose that
LuRhO may belong to the same novel class of non-Fermi liquids as
the nonmetallic metal FeCrAs.Comment: 11 pages, 5 figure
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