On The Unit Dot Product Graph Of A Commutative Ring

الموضوعات

علوم بحتة وطبيعية

الملخص

In 2015, Ayman Badawi (Badawi, 2015) introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 n < 1 be an integer, and R =A x A x ... x A (n times). We recall from (Badawi, 2015) that total dot product graph of R is the (undirected) graph TD(R) with vertices R* = R \ {(0, 0, ..., 0)}, and two distinct vertices x and y are adjacent if and only if xy = 0 [is an element of] A (where xy denote the normal dot product of x and y). Let Z(R) denotes the set of all zero-divisors of R. Then the zero-divisor dot product graph of R is the induced subgraph ZD(R) of TD(R) with vertices Z(R) = Z(R)* \ {(0, 0, ..., 0)}. Let U(R) denotes the set of all units of R. Then the unit dot product graph of R is the induced subgraph UD(R) of TD(R) with vertices U(R). Let n 2 and A = Zn. The main goal of this thesis is to study the structure of UD(R = A x A).

روابط وملفات

التعريف والنوع

رقم الوثيقة

edfb85f0-3c90-4474-8db6-8892555ffa78

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

45778_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"Ayman Badawi","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Mohammad Ahmad Abdulla","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

On The Unit Dot Product Graph Of A Commutative Ring

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

Ayman Badawi

الإعداد

Mohammad Ahmad Abdulla

الاقتباسات الببليوغرافية