Note on Larsen-McCarthy's multiplicative theory of ideals (Q2709723)

The Multiplicative theory of ideals [Pure Appl. Math. 43, Academic Press, New York-London (1971; Zbl 0237.13002)] by \textit{M. D. Larsen} and \textit{P. J. McCarthy} covers such basic topics in commutative ring theory as Noetherian rings and modules, primary decomposition, localization, integral dependence, valuation theory, dimension theory, Dedekind domains, Prüfer domains, Krull domains, and their generalizations. In this paper, the author goes through the above book theorem by theorem (excluding lemmas and propositions) and puts these theorems, where possible, into the context of commutative semigroups. There is also an appendix on root closed rings.