544 research outputs found
On solvable Dirac equation with polynomial potentials
One dimensional Dirac equation is analysed with regard to the existence of
exact (or closed-form) solutions for polynomial potentials. The notion of
Liouvillian functions is used to define solvability, and it is shown that
except for the linear potentials the equation in question is not solvable.Comment: 3 pages, updated bibliograph
Structure of semisimple Hopf algebras of dimension
Let be prime numbers with , and an algebraically closed
field of characteristic 0. We show that semisimple Hopf algebras of dimension
can be constructed either from group algebras and their duals by means
of extensions, or from Radford biproduct R#kG, where is the group
algebra of group of order , is a semisimple Yetter-Drinfeld Hopf
algebra in of dimension . As an application,
the special case that the structure of semisimple Hopf algebras of dimension
is given.Comment: 11pages, to appear in Communications in Algebr
On the Content of Polynomials Over Semirings and Its Applications
In this paper, we prove that Dedekind-Mertens lemma holds only for those
semimodules whose subsemimodules are subtractive. We introduce Gaussian
semirings and prove that bounded distributive lattices are Gaussian semirings.
Then we introduce weak Gaussian semirings and prove that a semiring is weak
Gaussian if and only if each prime ideal of this semiring is subtractive. We
also define content semialgebras as a generalization of polynomial semirings
and content algebras and show that in content extensions for semirings, minimal
primes extend to minimal primes and discuss zero-divisors of a content
semialgebra over a semiring who has Property (A) or whose set of zero-divisors
is a finite union of prime ideals. We also discuss formal power series
semirings and show that under suitable conditions, they are good examples of
weak content semialgebras.Comment: Final version published at J. Algebra Appl., one reference added,
three minor editorial change
Indecomposable modules and Gelfand rings
It is proved that a commutative ring is clean if and only if it is Gelfand
with a totally disconnected maximal spectrum. Commutative rings for which each
indecomposable module has a local endomorphism ring are studied. These rings
are clean and elementary divisor rings
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
A one-sided Prime Ideal Principle for noncommutative rings
Completely prime right ideals are introduced as a one-sided generalization of
the concept of a prime ideal in a commutative ring. Some of their basic
properties are investigated, pointing out both similarities and differences
between these right ideals and their commutative counterparts. We prove the
Completely Prime Ideal Principle, a theorem stating that right ideals that are
maximal in a specific sense must be completely prime. We offer a number of
applications of the Completely Prime Ideal Principle arising from many diverse
concepts in rings and modules. These applications show how completely prime
right ideals control the one-sided structure of a ring, and they recover
earlier theorems stating that certain noncommutative rings are domains (namely,
proper right PCI rings and rings with the right restricted minimum condition
that are not right artinian). In order to provide a deeper understanding of the
set of completely prime right ideals in a general ring, we study the special
subset of comonoform right ideals.Comment: 38 page
On indecomposable modules over the Virasoro algebra
It is proved that an indecomposable Harish-Chandra module over the Virasoro
algebra must be (i) a uniformly bounded module, or (ii) a module in Category
, or (iii) a module in Category , or (iv) a module which
contains the trivial module as one of its composition factors.Comment: 5 pages, Latex, to appear in Science in China
On maximal immediate extensions of valued division algebras
We show an extension theorem for strictly contracting bilinear mappings into a spherically complete valued vector space and we apply this result to prove that every maximal valued division algebra having the same characteristic as its residue division algebra is spherically complete
The Hopf modules category and the Hopf equation
We study the Hopf equation which is equivalent to the pentagonal equation,
from operator algebras. A FRT type theorem is given and new types of quantum
groups are constructed. The key role is played now by the classical Hopf
modules category. As an application, a five dimensional noncommutative
noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres
Twisted K-Theory of Lie Groups
I determine the twisted K-theory of all compact simply connected simple Lie
groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the
CFT prescription, and thus explains why it gives the correct result. Finally I
analyze the exceptions noted by Bouwknegt et al.Comment: 16 page
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