A Note on 2x2 Uniquely Clean Idempotent Matrices and Strongly Clean Matrices| Chapter 7 | Research Highlights in Mathematics and Computer Science Vol. 1

 A component of a ring is supposed to be spotless in the event that it is the amount of a unit and an idempotent. It is remarkably spotless assuming that this portrayal is novel. It is called emphatically spotless in the event that it is the amount of an idempotent and a unit that drive. It is notable that focal idempotents in any ring are extraordinarily perfect [1]. In this note it has been shown that the opposite is additionally obvious in 2M (R) , R an Essential Area. At the point when R is a projective free ring, a

 haracterization of emphatically clean components in ( ) n M R has been given [2]. At the point when R is a central ideal space (P.I.D.), towards such a portrayal we adopt a strategy which uses notable construction of idempotent lattices in ( ) n M R . We utilize this to describe non three-sided unequivocally clean components in 2 M (Z) concerning their entrances.

Author(s) Details:

Rafia Aziz,
Government Girls College, Khargone, M.P. - 451001, India.

K. N. Rajeswari,
School of Mathematics, Vigyan Bhawan, Khandwa Road, Indore - 452017, India.

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