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.