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Structure Theorem for B(1, 2) Bi-Near Rings |
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PP: 27-30 |
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doi:10.18576/sjm/040105
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Author(s) |
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S. Maharasi,
V. Mahalakshmi,
S. Jayalakshmi,
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Abstract |
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| In this paper, we introduce the concept of B(1, 2) S bi-near rings and give the structure theorem for the same. By N we mean a zero - symmetric bi-near ring. Balakrishnan [1] defined N to be a Pk(Pk) near-ring if xkN = xNx (Nxk = xNx) for all xN and a near-ring N is said to be a Pk(m, n) (Pk(m, n)) near - ring if xkN = xmNxn(Nxk = xmNxn) for all x N. Motivated by these concepts we introduce B(1,2) bi-near ring and their generalizations and similarities. A bi-near ring N is said to be a B(1, 2) bi-near ring if (a)rN = N(a)l2 for all aN1N2 where (a)r ((a)l) is the right (left) N- bisubgroup of a bi-near ring N generated by ‘a’. |
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