On strongly ∑-m-clean rings

Let m be a positive integer such that m ≥ 2 . In this paper, we define two new classes of rings called strongly ∑ - m -clean ring and m -semiboolean ring which are natural generalizations of the concept of strongly m -clean [ 13 ] and semiboolean [ 11 ], respectively. We exhibit connections between these rings and other related classes of rings. We examine the properties of these notions to various context of commutative ring extensions. The obtained results yield new original families of examples of rings subject to various ring theoretic properties.