فهرست نشریات علمی دسترسی آزاد ایران

In this paper, we prove that every element in an exchange ring $R$ with artinian primitive factors is $n$-tuplet-good iff $1_R$ is $n$-tuplet-good. Also, we show that for such rings the full matrix ring $M_n(R)$ (for $n\geq 2$) is $n$-tuplet-good. In [7], Fisher and Snider proved that every element of a strongly $\pi$-regular ring $R$ with $\frac{1}{2}\in R$ is 2-good. We prove the same result under new condition and show that these rings are twin-good. We also consider the conditions under which endomorphism ring of a finitely generated projective module $M$ over unit regular ring $L$ is 2-tuplet-good. The main result of [14] states that regular self-injective rings are $n$-tuplet-good if such rings has no factor ring isomorphic to a field $D$ with $|D|<n+2$. We generalized this result to regular Baer rings proving that every regular Baer ring $R$ that has no factor ring isomorphic to a field of order less than $n+2$, is $n$-tuplet-good.