Graded prime ideals over graded Lie algebras
Abdallah Shihadeh
TL;DR
This paper extends the concept of graded prime ideals from commutative graded rings to graded Lie algebras, exploring their properties and introducing related concepts like graded semiprime and total prime Lie ideals.
Contribution
It introduces the notion of graded prime ideals in graded Lie algebras and investigates their properties, expanding the theory beyond rings.
Findings
Properties of graded prime Lie ideals established
Introduction of graded semiprime and total prime Lie ideals
Analogies with prime ideals in rings demonstrated
Abstract
In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to those about graded prime ideals over a commutative or non-commutative ring.In addition, the ideas of graded semiprime Lie ideals and graded total prime Lie ideals will be introduced.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras