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σ-IDEALS OF ALMOST DISTRIBUTIVE LATTICES

M. Sambasiva Rao

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

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and

G. C. Rao

Department of Mathematics, Andhra University, Visakhapatnam-530003, India

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https://doi.org/10.1142/S179355711250057XCited by:1 (Source: Crossref)

Abstract

The concept of σ-ideals is introduced in almost distributive lattices (ADLs). Generalized stone ADLs are characterized in terms of their σ-ideals and α-ideals. Normal ADLs are also characterized in terms of their O-ideals and σ-ideals. Finally, a discussion is made about the epimorphic images and inverse images of σ-ideals.

Keywords:

AMSC: 06D99

References

G. Birkhoff , Lattice Theory , American Mathematical Society Colloquium Publications 25 ( American Mathematical Society , Providence, RI , 1967 ) . Google Scholar
G. C. Rao and M. S. Rao, Int. Math. Forum 4(15), 733 (2009). Google Scholar
G. C. Rao and M. S. Rao, European J. Pure Appl. Math. 2(1), 58 (2009). Google Scholar
G. C. Rao and M. S. Rao, Int. J. Contemp. Math. Sci. 4(10), 457 (2009). Web of Science, Google Scholar
G. C. Rao and M. S. Rao , Chamchuri J. Math. 3 , 13 ( 2011 ) . Web of Science, Google Scholar
G. C. Rao and S. Ravikumar , Southeast Asian Bull. Math. 32 , 831 ( 2008 ) . Google Scholar
G. C. Rao and S. Ravikumar, Int. J. Contemp. Math. Sci. 4(10), 475 (2009). Web of Science, Google Scholar
U. M. Swamy and G. C. Rao , J. Aust. Math. Soc. Ser. A 31 , 77 ( 1981 ) . Crossref, Web of Science, Google Scholar
U. M. Swamy , G. C. Rao and G. N. Rao , Southeast Asian Bull. Math. 27 , 513 ( 2003 ) . Google Scholar
U. M. Swamy , G. C. Rao and G. N. Rao , Southeast Asian Bull. Math. 27 , 1081 ( 2004 ) . Google Scholar