Abstract
The concept of E-squares introduced by Prof. K.S.S. Nambooripad plays an important role in the study of structure of Semigroups. Multiplicative semigroups of rings form an important class of semigroups and one theme in the study of semigroups is how the structure of this semigroup affects the structure of the ring. An important tool in analyzing the structure of a semigroup are the Green's relations. In this paper, we study some properties of these relations on the multiplicative semigroup of a regular ring and hence the properties of \(E\)-squares and \(\mathcal{D}\)-squares.
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