Polynomial fibre rings of algebras over noetherian rings.
p-Ranks of Class Groups in Zdp-Extensions.
Prescribing endomorphism algebras of -free modules
It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...
Prescribing endomorphism algebras. The cotorsion-free case
Projective modules and approximation couples
Pure submodules of multiplication modules.
Quadratic forms over rings of dimension 1.
Quantifier elimination for modules.
Quasi-basic submodules over valuation domains
Rank-two torsion-free modules over valuation domains
Regularly weakly based modules over right perfect rings and Dedekind domains
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.
Relations between Elements and p·1 for a Prime p
For any positive power n of a prime p we find a complete set of generating relations between the elements [r] = rⁿ - r and p·1 of a unitary commutative ring.
Relations between Elements r²-r
We prove that generating relations between the elements [r] = r²-r of a commutative ring are the following: [r+s] = [r]+[s]+rs[2] and [rs] = r²[s]+s[r].
Residual submodules of multiplication modules.
Ringepimorphismen und Morita-projektive Moduln über kommutativen Dedekind-Ringen.
Rings in Which Pure Ideals are Generated by Idempotents.
Rings Whose Modules Have Nice Decompositions.
-anneaux noethériens
S-divisible modules over domains.
Some new results on numbers of generators of ideals in local rings