Almost $\pi$-lattices
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 119-130
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we establish some conditions for an almost $\pi $-domain to be a $\pi $-domain. Next $\pi $-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for $\pi $-rings.
In this paper we establish some conditions for an almost $\pi $-domain to be a $\pi $-domain. Next $\pi $-lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for $\pi $-rings.
Classification : 06F05, 06F10, 13A15
Keywords: $\pi $-domain; almost $\pi $-domain; $\pi $-ring; $d$-prime element
@article{CMJ_2004_54_1_a10,
     author = {Jayaram, C.},
     title = {Almost $\pi$-lattices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {119--130},
     year = {2004},
     volume = {54},
     number = {1},
     mrnumber = {2040225},
     zbl = {1049.06012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a10/}
}
TY  - JOUR
AU  - Jayaram, C.
TI  - Almost $\pi$-lattices
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 119
EP  - 130
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a10/
LA  - en
ID  - CMJ_2004_54_1_a10
ER  - 
%0 Journal Article
%A Jayaram, C.
%T Almost $\pi$-lattices
%J Czechoslovak Mathematical Journal
%D 2004
%P 119-130
%V 54
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a10/
%G en
%F CMJ_2004_54_1_a10
Jayaram, C. Almost $\pi$-lattices. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 119-130. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a10/

[1] F.  Alarcon, D. D.  Anderson and C.  Jayaram: Some results on abstract commutative ideal theory. Period. Math. Hungar. 30 (1995), 1–26. | DOI | MR

[2] D. D.  Anderson: Abstract commutative ideal theory without chain condition. Algebra Universalis 6 (1976), 131–145. | DOI | MR | Zbl

[3] D. D.  Anderson, C.  Jayaram and P. A.  Phiri: Baer lattices. Acta. Sci. Math. (Szeged) 59 (1994), 61–74. | MR

[4] D. D.  Anderson and C.  Jayaram: Principal element lattices. Czechoslovak Math. J. 46(121) (1996), 99–109. | MR

[5] D. D.  Anderson and E. W.  Johnson: Dilworth’s principal elements. Algebra Universalis 36 (1996), 392–404. | DOI | MR

[6] R. P.  Dilworth: Abstract commutative ideal theory. Pacific J. Math. 12 (1962), 481–498. | DOI | MR | Zbl

[7] R. W.  Gilmer: Multiplicative Ideal Theory. Marcel Dekker, New York, 1972. | MR | Zbl

[8] W.  Heinzer and D.  Lantz: The Laskerian property in commutative rings. J. Algebra 72 (1981), 101–114. | DOI | MR

[9] C.  Jayaram and E. W.  Johnson: Almost principal element lattices. Internat. J. Math. Math. Sci. 18 (1995), 535–538. | DOI | MR

[10] C.  Jayaram and E. W.  Johnson: Some results on almost principal element lattices. Period. Math. Hungar. 31 (1995), 33–42. | DOI | MR

[11] C.  Jayaram and E. W.  Johnson: $s$-prime elements in multiplicative lattices. Period. Math. Hungar. 31 (1995), 201–208. | DOI | MR

[12] C.  Jayaram and E. W.  Johnson: Dedekind lattices. Acta. Sci. Math. (Szeged) 63 (1997), 367–378. | MR

[13] C.  Jayaram and E. W.  Johnson: $\sigma $-elements in multiplicative lattices. Czechoslovak Math.  J. 48(123) (1998), 641–651. | DOI | MR

[14] B. G.  Kang: On the converse of a well known fact about Krull donains. J. Algebra 124 (1989), 284–299. | DOI | MR

[15] M. D.  Larsen and P. J.  McCarthy: Multiplicative Theory of Ideals. Academic Press, New York, 1971. | MR

[16] K. B.  Levitz: A characterization of general ZPI-rings. Proc. Amer. Math. Soc. 32 (1972), 376–380. | MR

[17] P. J.  McCarthy: Principal elements of lattices of ideals. Proc. Amer. Math. Soc. 30 (1971), 43–45. | DOI | MR | Zbl

[18] N. K.  Thakare, C. S.  Manjarekar and S.  Maeda: Abstract spectral theory. II.  Minimal characters and minimal spectrums of multiplicative lattices. Acta. Sci. Math. (Szeged) 52 (1988), 53–67. | MR