InternationaleJournals

PO-r-FILTERSIN PO-r-SEMIGROUPS

 

 



VB Subrahmanyeswara Rao Seetamraju1, A. Anjaneyulu2, D. Madhusudana Rao3

1Dept. of Mathematics, V K R, V N B & A G K College of Engineering, Gudivada, A.P. India. Email Id: manyam4463@gmail.com

2Dept. of Mathematics, V S R & N V R College, Tenali, A.P. India. Email Id: anjaneyulu.addala@gmail.com

3Dept. of Mathematics, V S R & N V R College, Tenali, A.P. India. Email Id: dmrmaths@gmail.com

ABSTRACT

The terms left po-r-filter, right po-r-filter, po-r-filter, are introduced.  It is proved that a nonempty subset F of a po-r-semigroup S is a left po-r-filter if and only if  S/F is a completely prime right po-r-ideal of S or empty. Further it is proved that S is a po-r-semigroup and F is a left po-r-filter, then  S/F is a prime right po-r-ideal of S  or empty and A nonempty subset F of a commutative po-r-semigroup S is a left po-r-filter if and only if  S/F is a prime right po-r-ideal of S  or empty.  It is proved that a nonempty subset F of a po-r-semigroup S is a right po-r-filterif and only if  S/F is a completely prime left po-r-ideal of S or empty. It is proved that every po-r-filter F of a po-r-semigroupS is a po-c-system.  Further it is also proved that a nonempty subset F of a po-r-semigroup S is a po-r-filter if and only if S/F is a completely prime po-r-ideal of S or empty. It is provedthat every po-r-filter F of a po-r-semigroup S is a po-m-system.  It is proved that, if a nonempty subset F of a po-r-semigroup S is a po-r-filter, then F is a po-d-system of S or empty.  Further it is proved that, every po-r-filter F of a  po-r-semigroup S is a po-n-system of S.  It is proved that the po-r-filter of a po-r-semigroup S generated by a nonempty subset A of S is the intersection of all po-r-filters of S containing A.  It is proved that if N(b) N(a), then N(a)\N(b), if it is nonempty, is a completely prime po-r-ideal of N(a).

MATHEMATICS SUBJECT CLASSIFICATION (2010): 06F05, 06F99, 20M10, 20M99

KEY WORDS: po-r-semigroup, po-r-ideal, prime po-r-ideal, po-r-filter.

 

 

 


International eJournal of Mathematical Sciences, Technology and Humanities

Volume 2, Issue 4, Pages:  669 - 683