Dumitrescu, Tiberiu; Epure, Mihai Comaximal factorization lattices. (English) Zbl 1494.13022 Commun. Algebra 50, No. 9, 4024-4031 (2022). J. W. Brewer and W. J. Heinzer [Commun. Algebra 30, No. 12, 5999–6010 (2002; Zbl 1049.13002)] studied an integral domain \(D\) in which each nonzero ideal \(A\) can be written as a product \(A = Q_1 \cdots Q_n\), where the \(Q_i\) are pairwise comaximal and have the property that each \(Q_i\) has prime radical (resp., is primary, is prime powers).Now let \(\mathcal{I}(D)\) be the multiplicative monoid of proper (integral) ideals of an integral domain \(D\). Then \(\mathcal{I}(D)\) is a complete lattice and Brewer and Heinzer’s work is the factorization property of \(\mathcal{I}(D)\) as a lattice. In this paper, the authors extend the results of [loc. cit.] to a more general setting of multiplicative lattices with some additional properties such that \(\mathcal{I}(D)\) is contained in this class of lattices. Reviewer: Gyu Whan Chang (Incheon) MSC: 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations 06F99 Ordered structures 13A05 Divisibility and factorizations in commutative rings Keywords:comaximal factorization; multiplicative lattice; Dedekind lattice Citations:Zbl 1049.13002 PDFBibTeX XMLCite \textit{T. Dumitrescu} and \textit{M. Epure}, Commun. Algebra 50, No. 9, 4024--4031 (2022; Zbl 1494.13022) Full Text: DOI arXiv References: [1] Alarcon, F.; Anderson, D. D.; Jayaram, C., Some results on abstract commutative ideal theory, Period. Math. Hung, 30, 1-26 (1995) · Zbl 0822.06015 [2] Anderson, D. D., Abstract commutative ideal theory without chain conditions, Algebra Univ, 6, 131-145 (1976) · Zbl 0355.06022 [3] Anderson, D. D.; Cook, S. J., Two star operations and their induced lattices, Commun. Algebra., 28, 2461-2475 (2000) · Zbl 1043.13001 [4] Anderson, D. D.; Jayaram, C., Principal element lattices, Czech. Math. J, 46, 99-109 (1996) · Zbl 0898.06008 [5] Brewer, J.; Heinzer, W., On decomposing ideals into products of comaximal ideals, Commun. Algebra., 30, 5999-6010 (2002) · Zbl 1049.13002 [6] Dilworth, R., Abstract commutative ideal theory, Pacific J. Math, 12, 481-498 (1962) · Zbl 0111.04104 [7] El Baghdadi, S.; Gabelli, S.; Zafrullah, M., J. Pure Appl. Algebra., 212, 376-393 (2008) · Zbl 1131.13002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.