×

Join-principally generated multiplicative lattices. (English) Zbl 0547.06011

The paper deals with a multiplicative complete modular lattice which is a generalization of the classical ideal theory. It investigates the relationships between the various notions of ”principal”, the chain conditions, compactness assumptions, primary decompositions, the Principal Ideal Theorem and the Intersection Theorem.
Reviewer: H.Yutani

MSC:

06F10 Noether lattices
06B10 Lattice ideals, congruence relations
06F05 Ordered semigroups and monoids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D. D. Anderson,Abstract commutative ideal theory without chain conditions, Algebra Universalis6 (1976), 131-145. · Zbl 0355.06022 · doi:10.1007/BF02485825
[2] K. P. Bogart,Structure theorems for regular local Noether lattices, Michigan Math. J.15 (1968), 167-176. · Zbl 0162.03703 · doi:10.1307/mmj/1028999970
[3] ?,Distributive local Noether lattices, Michigan Math. J.16 (1969), 215-223. · Zbl 0188.04501 · doi:10.1307/mmj/1029000264
[4] R. P. Dilworth,Abstract commutative ideal theory, Pacific J. Math.12 (1962), 481-498. · Zbl 0111.04104
[5] D. G. Northcott,Ideal Theory, Cambridge University Press, New York, 1953. · Zbl 0052.26801
[6] M. Ward andR. P. Dilworth,Residuated lattices, Proceedings of the National Academy of Sciences24 (1938), 162-164. · Zbl 0018.29003 · doi:10.1073/pnas.24.3.162
[7] ? and ?, Residuated lattices, Trans. Amer. Math. Soc.45 (1939), 335-354. · JFM 65.0084.01 · doi:10.1090/S0002-9947-1939-1501995-3
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.