Remarks on special ideals in lattices
Beran, Ladislav
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 607-615 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. $D$-radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of $\hat C$-radicals. In addition, a necessary and sufficient condition for the equality of prime radicals is obtained.

Publié le : 1994-01-01
Classification:  06B10 
@article{118702,
     author = {Ladislav Beran},
     title = {Remarks on special ideals in lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {607-615},
     zbl = {0812.06002},
     mrnumber = {1321231},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118702}
}

Beran, Ladislav. Remarks on special ideals in lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 607-615. http://gdmltest.u-ga.fr/item/118702/

Beran L. Orthomodular Lattices (Algebraic Approach), Reidel Dordrecht (1985). (1985) | MR 0784029 | Zbl 0558.06008

Beran L. Distributivity in finitely generated orthomodular lattices, Comment. Math. Univ. Carolinae 28 (1987), 433-435. (1987) | MR 0912572 | Zbl 0624.06008

Beran L. On semiprime ideals in lattices, J. Pure Appl. Algebra 64 (1990), 223-227. (1990) | MR 1061299 | Zbl 0703.06003

Beran L. On the rhomboidal heredity in ideal lattices, Comment. Math. Univ. Carolinae 33 (1992), 723-726. (1992) | MR 1240194 | Zbl 0782.06007

Birkhoff G. Lattice Theory, 3rd ed., American Math. Soc. Colloq. Publ., vol. XXV, Providence, 1967. | MR 0227053 | Zbl 0537.06001

Chevalier G. Semiprime ideals in orthomodular lattices, Comment. Math. Univ. Carolinae 29 (1988), 379-386. (1988) | MR 0957406 | Zbl 0655.06008

Dubreil-Jacotin M.L.; Lesieur L.; Croisot R. Leçons sur la théorie des treillis, des structures algébriques ordonnées et des treillis géometriques, Gauthier-Villars Paris (1953). (1953) | MR 0057838 | Zbl 0051.26005

Rav Y. Semiprime ideals in general lattices, J. Pure Appl. Algebra 56 (1989), 105-118. (1989) | MR 0979666 | Zbl 0665.06006