On Completely And Semi Completely Prime Ideal With Respect To An Element Of A Boolean 1, 2 Near-Ring
Ameer A. J. AL Swidi
Keywords :1,2 near-ring,c.s.p.I,c.p.I,x-c.s.p.I,x-c.p.I
Abstract: In this paper ,I generalize concepts of 1,2 near-ring as well as of completely semi prime ideal with respect to an element x of a 1,2 near-ring and the completely prime ideal of a 1,2 near-ring with respect to an element x and the relationships between the completely prime ideal with respect to an element x of a 1,2 near-ring and some other types of ideals,as well as I will valid if I is c.p.I of 1,2 near-ring iff is a x-c.s.p.I of a 1,2 near-ring as well as valid if I is c.p.I of 1,2 near-ring iff is a x-c.s.p.I of 1,2 near-ring as well as I is e'-c.p.I of 1,2 near-ring iff it is a e'-c.s.p.I of 1,2 near-ring and all its valid after put condition of Boolean a 1,2 near-ring
 G.Birkenmeier,H.Heatherly and E.Lee,"Prime Ideals in Near-Ring",Results Math24(1993),27-48.
 G .Pilz"Near-Ring",North-Holland Publishing Company, Amsterdam-New York –oxford, 1983.
 Husein Hadi Abbass, Mohanad Ali Mohammed "On completely Prime Ideal with respect to an element of a Near-Ring",Journal of kerbala university , vol. 10 no.3 scientific . 2012,285-301 .
 Hussien Hadi Abass, Showq Mhammed .E"Completely Semi Prime Ideal With Respect to an Element of a Near Ring",Journal of Kufa for Mathematics and Computer, Vol.1, No.3, may , 2011, 1- 7 .
 H.A.S.Abujabal,"On structure and commutativity of Near-Rings",Antofagasta-Chile,2000.
 N.Groenewald,"The completely prime radical in Near-Rings",Acta Math.Hung.51(1988),301-305.
 N.J.Groenewald,"Different prime ideals in Near-Ring",comm.Algebra,19(10)(1991),2667-2675.
 S.uma,R.Balakrishnam,T.Tamizh"1,2near-ring international journal of algebra,vol.4,2010 ,no.2,71-79.
 W. B. Vasantha Kandasamy"smarandache Near-Rings",America Research Press and W.B. Vasantha Kandasamy,2002,19-23.
 W.M.L.Holcombe,"Primitive Near-Ring",doctoral Dissertation,university of Leeds,1970.