• CLOSED (OR OPEN) SUB NEAR-FIELD SPACES OF COMMUTATIVE NEAR-FIELD SPACE OVER NEAR-FIELD

Dr. N. V. NAGENDRAM

Abstract


Let N be a commutative near-field space with 1 ¹ 0, and let M be a proper sub near-field space of N. Recall that M is an n-absorbing sub near-field space if whenever x1, x2, ....,xn+1 ÎM for x1, x2, ....,xn+1ÎN, then there are n of the xi’s whose product is in M. We define M to be a semi-n-absorbing sub near-field space if xn+1 Î M for x Î N implies           xn Î M. More generally, for positive integers m and n, we define M to be close sub near-field space more specifically     (m, n)-closed sub near-field space if xmÎM for xÎN implies xn Î M. A number of examples and results on closed (or open) sub near-field spaces of commutative near-field space over a near-field.


Keywords


prime sub near-field space, radical near - field space, 2-absorbing sub near-field space, n - absorbing sub near-field space.

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