ISSN 2394-5125
 

Research Article 


Set Theoretic Implications of Projective Boolean Algebra

Dr. Abhay Kumar Lalan.

Abstract
This paper critically examines and compares different generalisation of projective Boolean algebras : such
as openly generated boolean algebras and tightly σ-filtered boolean algebras.
This paper shows here that for every uncountable regular cardinal K, there are 2K pair wise nonisomorphic
openly generated Boolean algebras of size K > ℵ, provided there is an almost free, non-free
abelean group of size K. Openly generated boolean algebras are almost free. Openly generated boolean
algebras are close to projective boolean algebras. Every openly generated boolean algebras of size ≤ ℵ, is
projective and it is non-trivial for tight σ-filterdness S-Koppelberg derived some significant results. Using
Koppelberg’s results some properties of projective boolean algebras may be generalized to lightly 6-filtered
boolean algebras. Openly generated boolean algebras have many relatively complete sub algebras and
tightly 6-filtered boolean algebras.

Key words: Implications, projective, isomorphic filtration tightness, embedding, epimorphism


 
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Pubmed Style

Dr. Abhay Kumar Lalan. Set Theoretic Implications of Projective Boolean Algebra. JCR. 2020; 7(5): 2865-2866. doi:10.31838/jcr.07.05.467


Web Style

Dr. Abhay Kumar Lalan. Set Theoretic Implications of Projective Boolean Algebra. http://www.jcreview.com/?mno=15239 [Access: August 17, 2021]. doi:10.31838/jcr.07.05.467


AMA (American Medical Association) Style

Dr. Abhay Kumar Lalan. Set Theoretic Implications of Projective Boolean Algebra. JCR. 2020; 7(5): 2865-2866. doi:10.31838/jcr.07.05.467



Vancouver/ICMJE Style

Dr. Abhay Kumar Lalan. Set Theoretic Implications of Projective Boolean Algebra. JCR. (2020), [cited August 17, 2021]; 7(5): 2865-2866. doi:10.31838/jcr.07.05.467



Harvard Style

Dr. Abhay Kumar Lalan (2020) Set Theoretic Implications of Projective Boolean Algebra. JCR, 7 (5), 2865-2866. doi:10.31838/jcr.07.05.467



Turabian Style

Dr. Abhay Kumar Lalan. 2020. Set Theoretic Implications of Projective Boolean Algebra. Journal of Critical Reviews, 7 (5), 2865-2866. doi:10.31838/jcr.07.05.467



Chicago Style

Dr. Abhay Kumar Lalan. "Set Theoretic Implications of Projective Boolean Algebra." Journal of Critical Reviews 7 (2020), 2865-2866. doi:10.31838/jcr.07.05.467



MLA (The Modern Language Association) Style

Dr. Abhay Kumar Lalan. "Set Theoretic Implications of Projective Boolean Algebra." Journal of Critical Reviews 7.5 (2020), 2865-2866. Print. doi:10.31838/jcr.07.05.467



APA (American Psychological Association) Style

Dr. Abhay Kumar Lalan (2020) Set Theoretic Implications of Projective Boolean Algebra. Journal of Critical Reviews, 7 (5), 2865-2866. doi:10.31838/jcr.07.05.467