DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

M. Sambasiva Rao

Mukkamala Sambasiva Rao

Department of Mathematics
MVGR College of Engineering, Vizianagaram
Andhra Pradesh, India-535005

email: mssraomaths35@rediffmail.com

0000-0002-1627-9603

Title:

Disjunctive inclusion property in pseudo-complemented distributive lattices

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-12-16 , Revised: 2023-04-14 , Accepted: 2023-04-14 , Available online: 2024-03-25 , https://doi.org/10.7151/dmgaa.1453

Abstract:

Disjunctive inclusion property of several prime ideals and prime filters of pseudo-complemented lattices is studied. Algebraic structures like Boolean algebras and Stone lattices are characterized with the help of the disjunctive inclusion property of prime ideals and prime filters. A set of equivalent conditions is given for every Stone lattice to become a Boolean algebra.

Keywords:

disjunctive inclusion property, minimal prime ideal, minimal prime filter, kernel ideal, $\delta $-ideal, Stone lattice, Boolean algebra

References:

  1. R. Balbes and A. Horn, Stone lattices, Duke Math. Journal 37 (1970) 537–545.
  2. G. Birkhoff, Lattice theory (Amer. Math. Soc. Colloq. XXV, Providence, U.S.A., 1967).
  3. T.S. Blyth, Ideals and filters of pseudo-complemented semi-lattices, Proc. Edin. Math. Soc. 23 (1980) 301–316.
  4. I. Chajda, R. Hala$\check{s}$ and J. K$\ddot{u}$hr, Semilattice structures (Heldermann Verlog, ISBN 978-3-88538-230-0, Germany, 2007).
  5. S.A. Celani, $\sigma $-ideals in distributive pseudo-complemented residuate lattices, Soft Computing 19(7) (2015) 1773–1777.
  6. W.H. Cornish, Congruences on distributive pseudo-complemented lattices, Bull. Austral. Math. Soc. 8 (1973) 161–179.
  7. W.H. Cornish, O-ideals, congruences and sheaf representation of distributive lattices, Rev. Roum. Math. Pures. et Appl. 22 (1977) 1059–1067.
  8. O. Frink, Pseudo-complements in semi-lattices, Duke Math. Journal 29 (1962) 505–514.
  9. G. Gratzer, General lattice theory (Academic press, New york, San Francisco, U.S.A, 1978).
  10. M. Sambasiva Rao, $\delta $-ideals in pseudo-complemented distributive lattices, Archivum Mathematicum 48(2) (2012) 97–105.
  11. M. Sambasiva Rao, Median prime ideals of pseudo-complemented distributive lattices, Archivum Mathematicum 58(4) (2022) 125–136.
  12. T.P. Speed, On Stone lattices, Jour. Aust. Math. Soc. 9(3-4) (1969) 297–307.
  13. M.H. Stone, A theory of representations for Boolean algebras, Tran. Amer. Math. Soc. 40 (1936) 37–111.
Close