Freely adjoining a complement to a lattice

George Grätzer; Harry Lakser

Mathematica Slovaca (2006)

  • Volume: 56, Issue: 1, page 93-104
  • ISSN: 0232-0525

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Grätzer, George, and Lakser, Harry. "Freely adjoining a complement to a lattice." Mathematica Slovaca 56.1 (2006): 93-104. <http://eudml.org/doc/32177>.

@article{Grätzer2006,
author = {Grätzer, George, Lakser, Harry},
journal = {Mathematica Slovaca},
keywords = {relative complement; free lattice; uniquely complemented},
language = {eng},
number = {1},
pages = {93-104},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Freely adjoining a complement to a lattice},
url = {http://eudml.org/doc/32177},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Grätzer, George
AU - Lakser, Harry
TI - Freely adjoining a complement to a lattice
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 1
SP - 93
EP - 104
LA - eng
KW - relative complement; free lattice; uniquely complemented
UR - http://eudml.org/doc/32177
ER -

References

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  1. ADAMS M. E- SICHLER J., Cover set lattices, Canad. J. Math. 32 (1980), 1177-1205. (1980) MR0596104
  2. ADAMS M. E.-SICHLER J., Lattices with unique complementation, Pacific. J. Math. 92 (1981), 1-13. (1981) Zbl0468.06005MR0618040
  3. CHEN C. C.-GRÄTZER G., On the construction of complemented lattices, J. Algebra 11 (1969), 56-63. (1969) Zbl0185.03701MR0232715
  4. CRAWLEY P.-DILWORTH R. P., Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, NJ, 1973. (1973) Zbl0494.06001
  5. DEAN R. A., Free lattices generated by partially ordered sets and preserving bounds, Canad. J. Math. 16 (1964), 136-148. (1964) Zbl0122.25801MR0157916
  6. DILWORTH R. P., Lattices with unique complements, Trans. Amer. Math. Soc. 57 (1945), 123-154. (1945) Zbl0060.06103MR0012263
  7. GRÄTZER G., General Lattice Theory, (2nd ed.), Birkhäuser Verlag, Basel, 1998 (Soft-cover edition Birkhauser Verlag, Basel-Boston-Berlin, 2003). (1998) Zbl0909.06002MR1670580
  8. GRÄTZER G., A reduced free product of lattices, Fund. Math. 73 (1971/72), 21-27. (1971) Zbl0229.06002MR0307986
  9. GRÄTZER G.-LAKSER H., Freely adjoining a relative complement to a lattice, Algebra Universalis 53 (2005), 189-210. Zbl1083.06011MR2148294
  10. GRÄTZER G.-LAKSER H., Embedding lattices into m-transitively complemented lattices, (Manuscript). 
  11. GRÄTZER G.-LAKSER H.-PLATT C. R., Free products of lattices, Fund. Math. 69 (1970), 233-240. (1970) Zbl0206.29703MR0274351
  12. HUNTINGTON E. V., Sets of independent postulates for the algebra of logic, Trans. Amer. Math. Soc. 79 (1904), 288-309. (1904) MR1500675
  13. LAKSER H., Free lattices generated by partially ordered sets, Ph.D. Thesis, University of Manitoba, 1968. (1968) MR2702904
  14. SALII V. N., Lattices with Unique Complements, Transl. Math. Monogr. 69, Amer. Math. Soc, Providence, RI. Zbl0632.06009MR0931777
  15. WHITMAN P. M., Free lattices. I; II, Ann. of Math. (2) 42; 43 (1941; 1942), 325-330; 104-115. (1941) MR0003614

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