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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2019 / Cilt: 19 - Sayı: 3

On Complete Sets of Orthogonal Idempotent of Rings for Which Homogeneous Maps are Linear

Homojen Fonksiyonları Lineer Olan Halkalara Tam Dik İdempotent Kümeler Üzerine

Necat GÖRENTAŞ
Pages
601–604
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The purpose of this work ispartly related to this question, but also to Show that the  ring classed deseribed above are not closedunder ring contrictions, and to give examples of rings with idempootents with infinite multiplicity ofidempotents outside the integral domain with comutative rings.In the next example, we present examples of the rings excluding non-trival idempotent

📌 3 Key Takeaways

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Objective & Hypothesis:Let R be a ring with identily.
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Key Findings & Data:If R has a complete set E of ortgonal idempotent with minimal size ofequivalence class ( ) 2 mE , then .
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Conclusion & Impact:The purpose of this work ispartly related to this question, but also to Show that the  ring classed deseribed above are not closedunder ring contrictions, and to give examples of rings with idempootents with infinite multiplicity ofidempotents outside the integral domain with comutative rings.In the next example, we present examples of the rings excluding non-trival idempotent
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let R be a ring with identily. If R has a complete set E of ortgonal idempotent with minimal size ofequivalence class ( ) 2 mE , then . R Question B in [1] asks if the conserve hold:If Ris ( ) 2 mE for any complete set G of orthogonal idempotent. The purpose of this work ispartly related to this question, but also to Show that the  ring classed deseribed above are not closedunder ring contrictions, and to give examples of rings with idempootents with infinite multiplicity ofidempotents outside the integral domain with comutative rings.In the next example, we present examples of the rings excluding non-trival idempotent

Özet

R birimli bir halka olsun. Eğer R ’de bir E tam dik idempotentler kümesi ve bu kümedeki en küçük denklik sınıfının eleman sayısı olan ( ) 2 mE ise R dir. [1]’deki B sorusu olan bu şartın gerek olup olmadığı sorulmaktadır. Yani; Rise R ’deki her tam dik idempotent E kümesi ( ) 2 mE midir? Bu çalışmanın amacı kısmen bu soru ile ilgili olmaklar birlikte aynı zamanda yukarıda tanımlanan R halka sınıflarının halka olmaları altında kapalı olmadığını göstermek ve komutatif halkalarla tamlık bölgeleri dışında ve sonsuz çoklukta idempotente sahip halka örnekleri ile aşikâr olmayan idempotentleri bulunamayan halka örneği vermektedir.

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Cite This Article

GÖRENTAŞ, N. (2022). On Complete Sets of Orthogonal Idempotent of Rings for Which Homogeneous Maps are Linear. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 19 - Sayı: 3, 601–604. https://ajindex.com/articles/429892

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References (3)

  1. Fuchs, P. Maxson C. J., Pilz, G., 1991. “On rings for which homogeneous maps are linear”, Proc.Amer. Math. Soc. 112, 1-7.
  2. Fuchs, P. R., 2000. On modules which force homogeneous maps to be linear. Proc. Amer. Math. Soc. 128(1), 5– 15. Jeconson, N., 1964.
  3. Structure of rings, Amer. Math. Soc. Collge publ. 37. Maxson, C. J.,; Van Der Merwe, A. B., 1998. Rings of homogeneous functions. J. Pure Appl. Algebra. 124(1-3), 211–226.