| Popis: |
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. Keywords-algebra, ideals of PU-algebra, G-part and P-radical of a PU-algebra, homomorphism of PU-algebra. |
