Fuzzy direct sums of fuzzy rings (Q1185032)

This paper continues the fuzzification of classical ring theory. More specifically the authors introduce the concepts of fuzzy weak direct sum and fuzzy complete direct sum of \(L\)-fuzzy subrings of an abelian ring where \(L\) denotes a complete distributive lattice. However most theorems are proved for lattices \(L\) that satisfy the so-called finite intersection property which means that the infimum of every subset of \(L\backslash\{0\}\) is greater than \(0\). Moreover all theorems are direct fuzzifications of the well-known classical results as mentioned in the book by \textit{O. Zariski} and \textit{P. Samuel} [Commutative algebra. Vol. I. Princeton etc.: van Nostrand (1958; Zbl 0081.26501)].