Nilpotent elements of skew Hurwitz series rings

Paykan, Kamal

doi:10.1007/s12215-016-0245-y

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Lemma 7 ([9])1

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Cited by 7 publications

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“…Lemma 8 (2.5 and 2.6 [17]). Let R be a σ-compatible NI-ring with nil(R) nilpotent and R a torsion free as a Z-module.…”

Section: Lemma 7 ([9])mentioning

confidence: 97%

Weak PS-rings over Skew Hurwitz Series

Farahat

Al-Bogamy²

2018

Eur. J. Pure Appl. Math.

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Abstract. The notion of PS-rings is extended to the class of weak PS-rings. We explore the algebraic properties of such class and study its relation with some other rings such as a local ring and a semisimple NI-ring. Also, we show the following result concerning, the ring of skew Hurwitz series, A = (HR, σ): Let R be a σ-compatible NI-ring with nil(R) nilpotent, σ(e) = e for every idempotent e ∈ R and R a torsion free as a Z-module. If R is a weak right PS-ring, then A = (HR, σ) is a weak right PS-ring.

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“…Lemma 8 (2.5 and 2.6 [17]). Let R be a σ-compatible NI-ring with nil(R) nilpotent and R a torsion free as a Z-module.…”

Section: Lemma 7 ([9])mentioning

confidence: 97%