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  • Author or Editor: Ebrahim Hashemi x
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A ring R is called right zip provided that if the right annihilator r R(X) of a subset X of R is zero, then there exists a finite subset Y of X, such that r R(Y) = 0. Faith [6] raised the following questions: When does R being a right zip ring imply R[x] being right zip?; When does R being a right zip imply R[G] being right zip when G is a finite group?; Characterize a ring R such that Mat n(R) is right zip. In this note we continue the study of the extensions of non-commutative zip rings based on Faith’s questions. It is shown that if R is a right McCoy ring, then R is right zip if and only if R[x] is a right zip ring. Also, if M is a strictly totally ordered monoid and R a right duo ring or a reversible ring, then R is right zip if and only if R[M] is right zip. As a consequence we obtain a generalization of [7].

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A ring R is called right principally quasi-Baer (or simply right p.q.-Baer ) if the right annihilator of a principal right ideal of R is generated by an idempotent. Let R be a ring such that all left semicentral idempotents are central. Let α be an endomorphism of R which is not assumed to be surjective and R be α -compatible. It is shown that the skew power series ring R [[ x; α ]] is right p.q.-Baer if and only if the skew Laurent power series ring R [[ x, x −1 ; α ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any countable family of idempotents in R has a generalized join in I ( R ). An example showing that the α -compatible condition on R is not superfluous, is provided.

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Aim

The aim of this study is to compare subcutaneous 5% dextrose versus subacromial corticosteroid injection for the treatment of chronic rotator cuff tendinopathy.

Methods

We carried out a randomized clinical trial with two parallel groups at a university hospital. Overall, 57 (32 women) were included in two groups of corticosteroid (n = 29) and dextrose (n = 28). The mean pain score was 6.6 (1.0). We used a visual analog scale for pain and goniometry for the range of motion. The measurements were repeated 1 month after the interventions. For corticosteroid, a single injection of triamcinolone and 1% lidocaine, and for dextrose, a mixture of 5% dextrose and 2% lidocaine three times weekly were prescribed.

Results

Both interventions were effective in decreasing pain compared to the baseline (both p < 0.001). The difference in pain between the two groups was nearly significant 1-month post-intervention (p = 0.052). The comparison of the two groups in considerable pain reduction (≥2.8) was in favor of dextrose (p = 0.046). The differences in the range of motion were not conclusive. None of the participants reported an important adverse effect.

Conclusion

The 5% dextrose treatment is at least as effective as corticosteroid for reducing pain in patients with rotator cuff tendinopathy.

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Abstract

The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R 0[x] equals to the set of all nilpotent elements of R 0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R 0[x] is a subset of the intersection of all maximal left ideals of R 0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R 0[x] coincides with the intersection of all maximal left ideals of R 0[x]. Moreover, we prove that the quasi-radical of R 0[x] is the greatest quasi-regular (right) ideal of it.

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