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Journals / Turkish Journal of Mathematics / 1996 / Cilt: 20 - Sayı: 4

Asosyatif diferensiyel halkalarda diferensiyel radikal idealler latisinin özellikleri ve asal radikalin diferensiyel analojisi

On a differential analog of the prime-radical and properties of the lattice of radical differential ideals in associative differential rings

Djavvat HADJIEV, Fethi ÇALLIALP

Pages
571–582
DOI
—

Abstract

In this paper we prove the following results: (1) For any assosiative differential ring with the unit we introduce a differential analog of the prime-radical and describe it; (2) any maximal differential ideal of a Ritt algebra is prime; (3) The lattice of radical differential ideals satisfies the condition of infinite $cap$- distributivity.

Özet

Bu çalışmada elde edilen temel sonuçlar:81) Birimli herhangi bir diferensiyel halkada, asal radikalin diferensiyel analojisini tanımlamak vekarakterize etmek, 82) Ritt cebirinin herhangi bir maksimal diferensiyel ideali asaldır, (3) radikal diferensiyel idealler latisi sonsuz $cap$-distribütif koşulunu sağlar.