On Mac Lane’s Conditions and Disjointness Properties for Posets

Jump To References Section

Authors

  • Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, Maharashtra ,IN
  • Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, Maharashtra ,IN

DOI:

https://doi.org/10.18311/jims/2024/30397

Keywords:

Mac Lane conditions, disjointness properties, Upper semimodular poset, Closed poset, LU-subposet.
06A06, 06B05, 06C10.

Abstract

In This Paper, We Generalized the Mac Lane’s Conditions And Disjointness Properties of Lattices for Posets and Relations Amongst Them Are Studied.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2024-01-01

How to Cite

Shewale, R. S., & Kharat, V. (2024). On Mac Lane’s Conditions and Disjointness Properties for Posets. The Journal of the Indian Mathematical Society, 91(1-2), 129–144. https://doi.org/10.18311/jims/2024/30397
Received 2022-06-06
Accepted 2024-01-08
Published 2024-01-01

 

References

G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Pub., Vol. 25, Third Edition, 1940.

G. Gr¨atzer, General Lattice Theory, Birkhauser Verlag, Second Edition, 1998.

L. Haskins and S. Gudder, Heights on posets and graphs, Discrete Math., 2 (1972), 357 - 382.

V. S. Kharat and B. N. Waphare, Reducibility in finite posets, European J. Combin., 22 (2001), no. 2, 197 - 205.

V. S. Kharat, B. N. Waphare and N. K. Thakare, On forbidden configurations for strong posets, Alg. Univ., 51 (2004), 111 - 124.

S. Mac Lane, A lattice formulations for transcendence degrees and p-bases, Duke Math. J., 4 (1938), 455 - 468.

F. Maeda and S. Maeda, Theory of Symmetric Lattices, Springer-Verlag, Berlin, Heidelberg, New York, 1970.

M. Saarim¨aki and P. Sorjonen, On Banaschewski functions in lattices, Alg. Univ., 28 (1991), 103 - 118.

M. Saarim¨aki, Disjointness of lattice elements, Math. Nachr., 159 (1992), 169 - 174.

R. S. Shewale and Vilas Kharat, Forbidden configurations for distributive, modular and semidistributive posets, Discrete Math., 339 (2016), 3005 - 3016.

R. S. Shewale and Vilas Kharat, Some Characterizations of Upper Semimodular Lattices and Posets, J. Indian Math. Soc. (N.S.), 82, Nos. (3 - 4) (2015), 189 - 205.

R. S. Shewale and Vilas Kharat, On modular pairs in posets, Asian-European Journal of Mathematics, 7, No. 3 (2014), 1450044 (30 pages).

M. Stern, Semimodular Lattices Theory and Applications, Cambridge University Press, 1999.

N. K. Thakare, S. Maeda and B. N. Waphare, Modular pairs, covering property and related results in posets, J. Indian Math. Soc. (N.S.), 70 (2003), 229 - 253.

N. K. Thakare, M. M. Pawar and B. N. Waphare, Modular pairs, standard elements, neutral elements and related results in posets, J. Indian Math. Soc. (N.S.), 71 (2004), 13 - 53.

B. N.Waphare and Vinayak Joshi, On Uniquely Complemented Posets, Order, 22 (2005), 11 - 20.