Regular Rank Rings

Abstract
1.1. Throughout this note, will denote an associative ring but we shall not require to possess a unit.If A and B are subsets of , then A + B will denote the set {x + y| xA, yB}. Aτ will denote the set {u ∊ | au = 0 for all aA} .Elements a and b will be said to be orthogonal if ab = ba = 0.

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