A Survey of Clean Elements in a Ring: Recent Advances
DOI:
https://doi.org/10.9734/bpi/ratmcs/v4/7284AKeywords:
Clean matrix, Diophantine equations, nil-clean matrix, uniquely nil-clean, strongly nil-clean, local ring, uniquely bleached ringAbstract
An element in a ring is called clean if it can be expressed as the sum of an idempotent element and a unit element of the ring. It is called strongly clean if it can be expressed as the sum of an idempotent element and a unit element of the ring which commute. It is called uniquely clean if there is only one way of representing it as the sum of an idempotent and a unit element in the ring. This paper contains an account of recently obtained results on clean, strongly clean and uniquely clean elements in a ring.
Published
2023-09-09
How to Cite
Rafia Aziz. (2023). A Survey of Clean Elements in a Ring: Recent Advances. Research and Applications Towards Mathematics and Computer Science Vol. 4, 73–85. https://doi.org/10.9734/bpi/ratmcs/v4/7284A
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