The classical left regular left quotient ring of a ring and its semisimplicity criteria
نویسنده
چکیده
Let R be a ring, CR and ′CR be the set of regular and left regular elements of R (CR ⊆ ′CR). Goldie’s Theorem is a semisimplicity criterion for the classical left quotient ring Ql,cl(R) := C −1 R R. Semisimplicity criteria are given for the classical left regular left quotient ring ′Ql,cl(R) := ′C −1 R R. As a corollary, two new semisimplicity criteria for Ql,cl(R) are obtained (in the spirit of Goldie).
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