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Register a new userIdempotent Elements in Multiplicative Lattices
العناصر الجامدة في الشبكات الضربية
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لدراسة الحلقات التبديلية بشكل مجرد، قام العالم دي لورث عام ١٩٦٢ ، بإدخال مفهوم الشبكات الضربية، و مفهوم العنصر الرئيس فيها و استخدام ذلك في تعريف الشبكات النيوثرية كمفهوم مجرد لشبكة المثاليات لحلقة نيوثرية، و قد أثبت فيها صحة العديد من الحقائق المعروفة في الحلقات النيوثرية. الغاية من هذا البحث هي إدخال مفهوم العنصر الجامد في الشبكات الضربية و دراسته، لما له من أهمية في دراسة الشبكات الضربية و في دراسة بعض الحلقات أيضًا كحلقات الزمر مثلا.
In ١٩٦٢ R.P.Dilworth introduced the concept of a Noether lattice as an abstraction of the concept of the lattice of ideals of a Noetherian ring. He showed that many of the important theorems of classical ideal theory held in them. The purpose of this paper is to introduce and study the concept of idempotent elements for the multiplicative lattices , since they play very idempotent role for studying the multiplicative lattices and some rings.
References used
ANDERSON,D.D.١٩٧٦ Multiplication ideals, Multiplication rings and the ring R(x) . Canad.J., math , ٢٨ , ٧٦٠-٧٦٨
DILWORTH, R.P.١٩٦٢ – Abstract commutative ideal theory. Pacific journal of Mathematics, ١٢, ٤٨٧-٤٩٨
JOHSON, E.W. and JOHSON. J.A.١٩٧٠ - Lattices modules over semi local Noether lattices. Fund Math ٦٨, ١٨٧-٢٠١
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