From a lattice to its ideal lattice

Kirby A. Baker; Alfred W. Hales

doi:10.1007/bf02485732

journal article Dec 01, 1974

From a lattice to its ideal lattice

Kirby A. Baker Alfred W. Hales

Algebra universalis Vol. 4 No. 1 pp. 250-258 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02485732

Topics

No keywords indexed for this article. Browse by subject →

References

24

[1]

K. A. Baker,Equational axioms for classes of lattices, Bull. Amer. Math. Soc.77 (1971), 97–102. 10.1090/s0002-9904-1971-12618-6

[2]

On the Structure of Abstract Algebras

Garrett Birkhoff

Mathematical Proceedings of the Cambridge Philosop... 1935 10.1017/s0305004100013463

[3]

G. Birkhoff,Lattice Theory, Amer. Math. Soc. Colloq. Publ.25 (1967).

[4]

A. Day,A simple solution to the word problem for lattices, Canad. Math. Bull.13 (1970), 253–254. 10.4153/cmb-1970-051-0

[5]

F. Galvin and B. Jónsson,Distributive sublattices of a free lattice, Canad. J. Math.13 (1961), 265–272. 10.4153/cjm-1961-022-8

[6]

H. S. Gaskill,On the relation of a distributive lattice to its lattice of ideals, Bull Austral. Math. Soc.7 (1972), 377–388. 10.1017/s0004972700045226

[7]

H. S. Gaskill, Thesis, Simon Fraser University.

[8]

H. S. Gaskill,On transferable semilattices, Algebra Universalis2 (1972) 303–316. 10.1007/bf02945041

[9]

G. Grätzer, ‘Universal algebra,’ inTrends in Lattice Theory, J. C. Abbott, ed., van Nostrand, Princeton, 1968.

[10]

G. Grätzer,Universal Algebra, van Nostrand, Princeton, 1968.

[11]

G. Grätzer,Lattice Theory: First Concepts and Distributive Lattices, Freeman, San Francisco, 1971.

[12]

G. Grätzer,A property of weakly transferable semilattices (preprint).

[13]

A. W. Hales,Partition representations of free lattices, Proc. Amer. Math. Soc.24 (1970), 517–520. 10.1090/s0002-9939-1970-0252289-0

[14]

B. Jónsson and J. E. Kiefer,Finite sublattices of a free lattice, Canad. J. Math.14 (1962), 487–497. 10.4153/cjm-1962-040-1

[15]

Equational bases and nonmodular lattice varieties

Ralph McKenzie

Transactions of the American Mathematical Society 1973 10.1090/s0002-9947-1972-0313141-1

[16]

E. Nelson,The embedding of a distributive lattice into its ideal lattice is pure (preprint).

[17]

R. S. Pierce,Introduction to the Theory of Abstract Algebras, Holt, Rinebart, and Winston, New York, 1968.

[18]

W. Poguntke and I. Rival,Finite sublattices generated by order-isomorphic subsets (preprint).

[19]

A. Robinson,Introduction, to Model Theory and to the Metamathematics of Algebra, 2nd. ed., North-Holland Publ. Co. Amsterdam, 1965.

[20]

A. Robinson,Non-standard Analysis, North-Holland Publ. Co., Amsterdam, 1966.

[21]

D. Sachs,Identities in finite partition lattices, Proc. Amer. Math. Soc.12 (1961), 944–945. 10.1090/s0002-9939-1961-0133267-3

[22]

P. Whitman,Free lattices, Ann. of Math.42 (1941), 325–329. 10.2307/1969001

[23]

P. Whitman,Free lattices, II, Ann. of Math.43 (1942), 104–115. 10.2307/1968883

[24]

P. Whitman,Lattices, equivalence relations, and subgroups, Bull. Amer. Math. Soc.52 (1946), 507–522. 10.1090/s0002-9904-1946-08602-4

Metrics

22

Citations

24

References

Details

Published: Dec 01, 1974
Vol/Issue: 4(1)
Pages: 250-258
License: View

Authors

Cite This Article

Kirby A. Baker, Alfred W. Hales (1974). From a lattice to its ideal lattice. Algebra universalis, 4(1), 250-258. https://doi.org/10.1007/bf02485732

From a lattice to its ideal lattice

You May Also Like