This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature. Wide-ranging developments in commutative ring theory are examined.

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Background and preliminaries on zero-dimensional rings
zero-dimensionality and products of commutative rings
zero-dimensional extension rings and subrings
residue fields of zero-dimensional rings
dimensions of extension rings
Picard groups,cancellation and the multiplicative structure of fields
derivations and deformations of zero-dimensional rings and algebras
the ring R[X,r/X]
P.M. Cohn's completely primal elements
some factorization properties of the ring of integer-valuedpolynomials
on the nonuniversality of
weak normalization
a visit to valuation and pseudo-valuation domains
answer to a question on the principal idea theorem
on the Davenport constant, the cross number, and their application in factorization theory
the Picard group of a polynomial ring
integral extensions with fibers of prescribed cardinality
homological dimensions of localizations of polynomial rings
splitting rings for p-local torsion-free groups
prime ideals in birational extensions ofpolynomial rings II
duals of ideals in pullback constructions
cancellation and prime spectra
the ascending chain condition on n-generated submodules
more almost Dedekind domains and Prufer domains of polynomials
direct limits of finite products offields
Eisenstein-type irreducibility criteria
on integer-valued polynomials
the prime spectrum of an infinite product of zero dimensional rings
when is a self-injective ring zero-dimensional

some problems in commutative ring theory.