It is proved that a ring R in which for every x ∈ R there exists a (and hence
the smallest) natural number n(x) > 1 such that xn(x) = x is always a Smarandache
Ring. Two examples are provided for justification

Chandra Sekhar Rao, A.K.S.

Srinivas, T.

ZENODO

English

Alegbra, Reading Mass: Addison –Wesely, World student Series Edition,

Basic Algebra, Vol. I & II

Direct Sum Decomposition of Atomic and Orthogonally Complete Rings;

Introduction to Lattice Theory,

Rao A.K.S.: Contributions to Theory of Rings, Doctoral Thesis,

Smarandache Algebraic structures,

Special Algebraic Structures in collected papers,

Structure of Rings;

Vasantha Kandasamy W.B: Smarandache Rings,

W.B: Groupoids and Smarandache groupoids,

W.B: Smarandache Semi groups,

W.B.: Smarandache Semi rings and Smarandache Semi fields,

ON SMARANDACHE RINGS