Research Article

New View of Ideals on PU-Algebra

by  Samy M. Mostafa, Mokhtar A. Abdel Naby, Alaa Eldin I. Elkabany
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 111 - Issue 4
Published: February 2015
Authors: Samy M. Mostafa, Mokhtar A. Abdel Naby, Alaa Eldin I. Elkabany
10.5120/19524-1153
PDF

Samy M. Mostafa, Mokhtar A. Abdel Naby, Alaa Eldin I. Elkabany . New View of Ideals on PU-Algebra. International Journal of Computer Applications. 111, 4 (February 2015), 9-15. DOI=10.5120/19524-1153

                        @article{ 10.5120/19524-1153,
                        author  = { Samy M. Mostafa,Mokhtar A. Abdel Naby,Alaa Eldin I. Elkabany },
                        title   = { New View of Ideals on PU-Algebra },
                        journal = { International Journal of Computer Applications },
                        year    = { 2015 },
                        volume  = { 111 },
                        number  = { 4 },
                        pages   = { 9-15 },
                        doi     = { 10.5120/19524-1153 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2015
                        %A Samy M. Mostafa
                        %A Mokhtar A. Abdel Naby
                        %A Alaa Eldin I. Elkabany
                        %T New View of Ideals on PU-Algebra%T 
                        %J International Journal of Computer Applications
                        %V 111
                        %N 4
                        %P 9-15
                        %R 10.5120/19524-1153
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

In this manuscript, we introduce a new concept, which called PU-algebra X . We state and prove some theorems about fundamental properties of it. Moreover ,we give the concepts of a weak right self-maps, weak left self-maps and investigated some its properties. Further, we have proved that every associative PU-algebra is a group and every p-semisimple algebra is an abelian group. We define the centre of a PU-algebra X and show that it is a p-semisimple sub-algebra of X, which consequently implies that every PU-algebra contains a p-semisimple PU-algebra . Furthermore, we give the concepts of ideals ( -ideals , i=1,2,3,4) in PU-algebra , classified they into classes correspond to various formula and we have proved that, they are coincide . Mathematics Subject Classification: 06F35, 03G25, 08A30.

References
  • Q. P. Hu, X. Li, On BCH-algebras, Mathematics Seminar Notes 11 (1983) 313–320.
  • Y. Imai, K. Iseki, On axiom systems of propositional calculi, XIV Proceedings of Japan Academy 42 (1966) 19–22.
  • H. S. Kim, Y. H. Kim, On BE-algebras, Scientiae Mathematicae Japonica Online, e-2006, 1299–1302.
  • K. Megalai and A. Tamilarasi, Classification of TM-algebra, IJCA Special Issue on "Computer Aided Soft Computing Techniques for Imaging and Biomedical Applications" CASCT. 2010.
  • B. L. Meng, CI-algebra, Scientiae Mathematicae Japonica Online, e-2009, 695-701.
  • S. M. Mostafa, M. A. Abd-Elnaby and M. M. M. Yousef, Fuzzy ideals of KU-Algebras, International Mathematical Forum, 6(63) (2011) 3139-3149.
  • J. Neggers, H. S. Kim, On d-algebras, Mathematica Slovaca 49 (1999) 19–26.
  • J. Neggers, S. S. Ahn, H. S. Kim, On Q-algebras, International Journal of Mathematics & Mathematical Sciences 27 (2001) 749–757.
  • C. Prabpayak and U. Leerawat, On ideas and congurences in KU-algebras, Scientia Magna Journal, 5(1) (2009) 54-57.
  • C. Prabpayak and U. Leerawat, On isomorphisms of KU-algebras, Scientia Magna Journal, 5(3) (2009) 25-31
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

PU-algebra ideals of PU-algebra G-part and P-radical of a PU-algebra homomorphism of PU-algebra.

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