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Keywords:
primary element; compactly packed lattice; Laskerian lattice
primary element; compactly packed lattice; Laskerian lattice
Summary:
In this paper we investigate prime divisors, $B_w$-primes and $zs$-primes in $C$-lattices. Using them some new characterizations are given for compactly packed lattices. Next, we study Noetherian lattices and Laskerian lattices and characterize Laskerian lattices in terms of compactly packed lattices.
References:
[1] F. Alarcon, D. D. Anderson and C. Jayaram: Some results on abstract commutative ideal theory. Period. Math. Hungar. 30 (1995), 1–26. DOI 10.1007/BF01876923 | MR 1318850
[2] D. D. Anderson: Abstract commutative ideal theory without chain condition. Algebra Universalis 6 (1976), 131–145. DOI 10.1007/BF02485825 | MR 0419310 | Zbl 0355.06022
[3] D. D. Anderson, J. Matigevic and W. Nichols: The Krull Intersection Theorem II. Pacific J. Math. 66 (1976), 15–22. DOI 10.2140/pjm.1976.66.15 | MR 0435062
[4] D. D. Anderson and E. W. Johnson: Dilworth’s principal elements. Algebra Universalis 36 (1996), 392–404. DOI 10.1007/BF01236764 | MR 1408734
[5] J. T. Arnold and J. W. Brewer: Commutative rings which are locally Noetherian. J. Math. Kyoto Univ. 11-1 (1971), 45–49. MR 0271086
[6] R. P. Dilworth: Abstract commutative ideal theory. Pacific J. Math. 12 (1962), 481–498. DOI 10.2140/pjm.1962.12.481 | MR 0143781 | Zbl 0111.04104
[7] R. W. Gilmer and W. Heinzer: The Laskerian property, power series rings and Noetherian spectra. Proc. Amer. Math. Soc. 79 (1980), 13–16. DOI 10.1090/S0002-9939-1980-0560575-6 | MR 0560575
[8] W. Heinzer and J. Ohm: Locally Noetherian commutative rings. Tran. Amer. Math. Soc. 158 (1971), 273–284. DOI 10.1090/S0002-9947-1971-0280472-2 | MR 0280472
[9] W. Heinzer and D. Lantz: The Laskerian property in commutative rings. J. Algebra 72 (1981), 101–114. DOI 10.1016/0021-8693(81)90313-6 | MR 0634618
[10] C. Jayaram and E. W. Johnson: $s$-prime elements in multiplicative lattices. Period. Math. Hungar. 31 (1995), 201–208. DOI 10.1007/BF01882195 | MR 1610262
[11] J. Ohm and R. L. Pendleton: Rings with Noetherian spectrum. Duke Math. J. 35 (1968), 631–639. DOI 10.1215/S0012-7094-68-03565-5 | MR 0229627
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