Abstract
In this paper, we explore locally principal element lattices in terms of primary, semiprimary and prime power elements.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.D. Anderson, Abstract commutative ideal theory without chain condition,Algebra Universalis 6 (1976), 131–145.
D.D. Anderson, C. Jayaram andF. Alarcon, Some results on abstract commutative ideal theory,Per. Math. Hung. 30 (1995), 1–26.
H.S. Butts andR.C. Phillips, Almost multiplication rings,Can J. Math. 17 (1965), 267–277.
R.P. Dilworth, Abstract commutative ideal theory,Pacific J. Math. 12 (1962), 481–498.
R. Gilmer andJ.J. Mott, Multiplication rings in which ideals with prime radical are primary,Trans. Amer. Math. Soc.,114 (1965), 40–52.
R. Gilmer, Some containment relations between of ideals of a commutative ring,Pacific J. Math. 15 (1965), 497–502.
C. Jayaram andE. W. Johnson, Almost principal element lattices,Intl. J. Math. 10 (1995), 535–539.
E.W. Johnson andJ.P. Lediaev, Representable distributive Noether lattices,Pacific J. Math. 28 (1969), 561–564.
E.W. Johnson andJ.A. Johnson,P-lattices as ideal and submodule lattices,Commen. Math. Univ. San Pauli 38 (1989), 21–27.
W. Krull, Idelatheorie in Ringen ohne Endlichkeitsbedingung,Math. Ann. 101 (1929), 729–744.
M.D. Larsen andP.J. MacCarthy,Multiplicative Theory of Ideals, Academic Press, New York, 1971.
S. Mori, Über allgemeine Multiplikationsringe II,J. Sci. Hiroshima Univ. Ser. A 4 (1934), 1–26.
S. Mori, Über Idealtheorie der Multiplikationsringe,J. Sci. Hiroshima Univ. Ser. A 19 (1956), 429–437.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jayaram, C., Johnson, E.W. Some results on almost principal element lattices. Period Math Hung 31, 33–42 (1995). https://doi.org/10.1007/BF01876351
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01876351