Groupoids in Involution Rings

P.G. Romeo and K.K. Sneha

Describing the structure of certain special types of elements in a ring (in fact in any algebraic structure) is an interesting problem in structure theory. This study was performed to carry out some properties of partial isometries and Moore-penrose invertible elements and the structure of partial isometries and Moore-penrose invertible elements in an involution ring. It is shown that partial isometries in an involution ring is an ordered groupoid and is a sub-groupoid of the groupoid of Moore-penrose invertible elements in R.

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