Published October 23, 2023
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$$\delta $$-ideals of p-algebras
- 1. Tanta University
- 2. South Valley University
Description
Abstract In p -algebras, the concepts of $$\delta $$ δ -ideals and principal $$\delta $$ δ -ideals are presented, and some of their respective properties are discussed. It is observed that the set $$I^{\delta }(L)$$ I δ ( L ) of all $$\delta $$ δ -ideals of a p -algebra L is a bounded lattice, and the class $$I_{p}^{\delta }(L)$$ I p δ ( L ) of all principal $$\delta $$ δ -ideals forms a bounded sublattice of $$I^{\delta }(L)$$ I δ ( L ) and a Boolean algebra on its own. A characterization of a $$\delta $$ δ -ideal in terms of principal $$\delta $$ δ -ideals, in p -algebras, is given. Also, the concept of comaximality of $$\delta $$ δ -ideals is discussed in p -algebras. After that, a number of properties of the homomorphic image of $$\delta $$ δ -ideals are considered.
Translated Descriptions
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This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
Abstract In p - algebras, the concepts of $$\delta $$ δ - ideals and principal $$\ delta $$ δ - ideals are presented, and some of their respective properties are discussed. من الملاحظ أن المجموعة $$I^{\delta }( L )$$ I δ ( L ) من جميع $$\ delta $$ δ - Idals of a p - algebra L عبارة عن مطاط محدود، وأن الفئة $$I _{ p }^{\delta }( L )$$$ I p δ ( L ) من جميع المبادئ الأساسية $$\ delta $$ δ - Idals تشكل طبقة فرعية محدودة من $$I^{\delta }( L )$$$ I δ ( L ) وجبر منطقي من تلقاء نفسها. يتم إعطاء توصيف لـ $$\ delta $$ δ - مثالي من حيث أصل $$\ delta $$ δ - مثالي، في p - algebras. أيضا، تتم مناقشة مفهوم comaximality من $$\ delta $$ δ - ideals في p - algebras. بعد ذلك، يتم النظر في عدد من خصائص الصورة المتجانسة $$\delta $$ δ - Idals.Translated Description (English)
Abstract In p -algebras, the concepts of $$\delta $$ δ -ideals and principal $$\delta $$ δ -ideals are presented, and some of their respective properties are discussed. It is observed that the set $$I^{\delta }(L)$$ I δ ( L ) of all $$\delta $$ δ -ideals of a p -algebra L is a bounded latex, and the class $$I_{p}^{\delta }(L)$$ I p δ ( L ) of all principal $$\delta $$ δ -ideals forms a bounded sublattice of $$I^{\delta }(L)$$ I δ ( L ) and a Boolean algebra on its own. A characterization of a $$\delta $$ δ -ideal in terms of principal $$\delta $$ δ -ideals, in p -algebras, is given. Also, the concept of comaximality of $$\delta $$ δ -ideals is discussed in p -algebras. After that, a number of properties of the homomorphic image of $$\delta $$ δ -ideals are considered.Translated Description (French)
Résumé Dans p -algebras, les concepts de $$\delta $$ δ -idéaux et de $$\delta $$ δ -idéaux principaux sont présentés, et certaines de leurs propriétés respectives sont discutées. On observe que l'ensemble $$I^{\delta }(L)$$ I δ ( L ) de tous les $$\delta $$ δ -idéaux d'une p -algèbre L est un latex borné, et la classe $$I_{p}^{\delta }(L)$$ I p δ ( L ) de tous les $$\delta $$ δ -idéaux principaux forme un sous-réseau borné de $$I^{\delta }(L)$$ I δ ( L ) et une algèbre booléenne seule. Une caractérisation d'un $$\delta $$ δ -idéal en termes de $$\delta $$ δ -idéaux principaux, en p -algèbres, est donnée. De plus, le concept de comaximalité des $$\delta $$ δ -idéaux est discuté dans p -algèbres. Après cela, un certain nombre de propriétés de l'image homomorphe de $$\delta $$ δ -idéaux sont considérées.Translated Description (Spanish)
Resumen En p -álgebras se presentan los conceptos de $$\delta $$ δ -ideales y principal $ $\delta $ $ δ -ideales, y se discuten algunas de sus respectivas propiedades. Se observa que el conjunto $$I^{\delta }(L)$$ I δ ( L ) de todos los $$\delta $$ δ -ideales de una p -álgebra L es un látex acotado, y la clase $$I_{p}^{\delta }(L)$$ I p δ ( L ) de todos los $$\delta $$ δ -ideales principales forma un sublátex acotado de $$I^{\delta }(L)$$ I δ ( L ) y un álgebra de Boole por sí sola. Se da una caracterización de un $ $\delta $ $ δ -ideal en términos de principal $ $\delta $ $ δ -ideal, en p -álgebras. Además, el concepto de comaximalidad de $$\delta $$ δ -ideales se discute en p -álgebras. Después de eso, se consideran una serie de propiedades de la imagen homomórfica de $ $\delta $ $ δ -ideales.Files
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Additional details
Additional titles
- Translated title (Arabic)
- $$\ delta $$- مثالية لـ p - algebras
- Translated title (English)
- $$\delta $$-ideals of p-algebras
- Translated title (French)
- $$\delta $$-idéauxdes algèbres p
- Translated title (Spanish)
- $$\delta $$-ideales de p-álgebras
Identifiers
- Other
- https://openalex.org/W4387880137
- DOI
- 10.1007/s00500-023-09308-0
References
- https://openalex.org/W1969054790
- https://openalex.org/W2034642607
- https://openalex.org/W2080615429
- https://openalex.org/W2093397547
- https://openalex.org/W2735103897
- https://openalex.org/W3134823879
- https://openalex.org/W4245326231
- https://openalex.org/W4380682514