شماره ركورد كنفرانس :
3735
عنوان مقاله :
Relative Annihilators in BCI-algebras
پديدآورندگان :
Banderi Ali a-banderi@phdst.scu.ac.ir Shahid Chamran University of Ahvaz , Harizavi Habib harizavi@scu.ac.ir Shahid Chamran University of Ahvaz
كليدواژه :
BCI , algebra , relative annihilator , normal ideal , relative pseudocomplement , boolean lattice
عنوان كنفرانس :
اولين كنفرانس منطقه اي علوم رياضي و كاربردها
چكيده فارسي :
In this paper, for any two subsets A and C of a BCI-algebra X, the concept of relative annihilator of A with respect to C, denoted by (C:A), is introduced and some related properties are investigated. Using this concept, some necessary and sufficient conditions for a BCI-algebra to be p-semisimple is established.
Moreover, for any normal ideal A and ideal C of a BCI-algebra X, it is proved that (C:A) is the relative pseudocomplement of A with respect to C.
Finally, applying the concept of relative annihilator, the involutory ideal with respect to an ideal is defined and it is shown that the set of all involutory ideals with respect to a normal ideal forms a complete and complemented lattice