Zhen Lei
Abstract
If a ring R is generalized regular ring,then following conditions are shown to be equivalent: (1)R is strongly regular ring;(2)E(R)C(R);(3)ex=xe,for all e∈E(R),all x∈N(R);(4)N(R)C(R);(5)E(R) is closed under the multiplication in R;(6)E(R) is a weakly commutative.
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If a ring R is generalized regular ring,then following conditions are shown to be equivalent: (1)R is strongly regular ring;(2)E(R)C(R);(3)ex=xe,for all e∈E(R),all x∈N(R);(4)N(R)C(R);(5)E(R) is closed under the multiplication in R;(6)E(R) is a weakly commutative.
Key concepts: Commutative ring, Ring (chemistry), Mathematics, Multiplication (music), Regular ring, Reduced ring, Combinatorics, Von Neumann regular ring