Tree Pattern Queries (TPQ), Branching Path Queries (BPQ), and Core XPath (CXPath) are subclasses of the XML query language XPath, TPQ ⊂ BPQ ⊂ CXPath ⊂ XPath. Let TPQ = TPQ ⊂ BPQ ⊂ CXPath ⊂ XPath denote the corresponding subclasses, consisting of queries that do not involve the boolean negation operator not in their predicates. Simulation and bisimulation are two different binary relations on gr...

Let V be a finite-dimensional representation of a finite group G of order n over a field k. Then by a classical theorem of Hermann Weyl [5] on polarizations one obtains a nice generating set for the invariant ring (SymV ) consisting of er(f), r = 1, 2, . . . , n, f ∈ V ∗ where er(f) denotes the r-th elementary symmetric polynomial in σ.f, σ ∈ G. Also, for any point x ∈ P(V ) there is a G-invari...

Hyperkähler Analogues of Kähler Quotients by Nicholas James Proudfoot Doctor of Philosophy in Mathematics University of California, Berkeley Professor Allen Knutson, Chair Let X be a Kähler manifold that is presented as a Kähler quotient of Cn by the linear action of a compact group G. We define the hyperkähler analogue M of X as a hyperkähler quotient of the cotangent bundle T ∗Cn by the induc...

In this paper we initiate a new approach consisting to characterize the commutativity of quotient ring $R/P$ by endomorphisms $R$ satisfying some algebraic identities involving prime ideal $P.$ Some well-known results concerning (semi-prime) rings have been improved.

We investigate the Cox ring of a normal complete variety X with algebraic torus action. A first result relates the Cox ring of X to that of a maximal geometric quotient of X. As a consequence, we obtain a complete description of the Cox ring in terms of generators and relations for varieties with torus action of complexity one. Applied to smooth K-surfaces, this gives a description of the Cox r...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

Following Weyl’s account in The Classical Groups we develop an analogue of the (first and second) Fundamental Theorems of Invariant Theory for rings of differential operators: when V is a k-dimensional complex vector space with the standard SLkC action, we give a presentation of the ring of invariant differential operators D(C[V n])SLkC and a description of the ring of differential operators on...

We study the free Lie ring of rank 2 in the variety of all centreby-nilpotent-by-abelian Lie rings of derived length 3. This is the quotient L/([γc(L′), L] + L′′′) with c > 2 where L is the free Lie ring of rank 2, γc(L′) is the c-th term of the lower central series of the derived ideal L′ of L, and L′′′ is the third term of the derived series of L. We show that the quotient γc(L′) + L′′′/[γc(L...

Ayache has recently proved that if R is an integrally closed domain such that each overring of R is treed, then R is a locally pseudo-valuation domain. We investigate the extent to which the analogue (in which one concludes that R is a locally pseudo-valuation ring) holds if R is generalized to a commutative ring. A positive result is obtained if R is an idealization D(+)K where D is an integra...