Our goal is to establish an efficient decomposition of an ideal A of a commutative ring R as an intersection of primal ideals. We prove the existence of a canonical primal decomposition: A = ⋂ P∈XA A(P ), where the A(P ) are isolated components of A that are primal ideals having distinct and incomparable adjoint primes P . For this purpose we define the set Ass(A) of associated primes of the id...

Decision-theoretic planning with risk-sensitive planning objectives is important for building autonomous agents or decisionsupport agents for real-world applications. However, this line of research has been largely ignored in the artificial intelligence and operations research communities since planning with risksensitive planning objectives is much more complex than planning with risk-neutral ...

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...

A closed 4-manifold (or, more generally, a finite PD4space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD3-complex. A Poincaré duality space is a space X of the homotopy type of a cell complex which satisfies Poincaré duality w...

Recently several different homological finitenes conditions have been introduced for monoids. I will survey the interplay between these notions. It is, in fact, more natural (and more illuminating) to work in the wider context of associative algebras.

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa...

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

We consider locally finite geometries of rank 3 belonging to certain diagrams where all strokes represent classes of non-trivial designs, at least one of them consisting of symmetric designs other than projective planes. The gonality diagram of such geometry is of spherical type, whereas the diameter diagram is of affine type. In cases like this, the criteria available from 24 cannot tell us an...

Abstract We present necessary and sufficient conditions for the finiteness of moments a fixed order generalized statistics based on an arbitrary life baseline distribution with finite expectation. The depend relation between moment minimal parameter statistic its multiplicity. Furthermore, under these we determine sharp upper bounds expressed in scale units being respective powers mean distribu...