-
- Active Topics
-
-
- by Eli 1 day ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 332 Views 40510
- by Eli 1 day ago Iran's President Ebrahim Raisi Aged 63 Dies in a Helicopter Crash View the latest post Replies 3 Views 63
- by Eli 1 day ago Re: What is in Your Mind? View the latest post Replies 717 Views 307276
- by Eli 3 days ago PySpark for Large Data Processing View the latest post Replies 2 Views 8172
- by Eli 3 days ago Online Bible View the latest post Replies 3 Views 23331
- by Eli 3 days ago Generating SSH Key and Adding it to the ssh-agent for Authentication on GitHub View the latest post Replies 1 Views 488
- by Eli 1 week ago Russia Invades Ukraine View the latest post Replies 663 Views 241111
- by Eli 2 weeks ago President Museveni's Speech During International Development Association (IDA) Summit View the latest post Replies 1 Views 509
- by Eli 2 weeks ago From Simple Linear Regression Analysis to Covariance & Correlation to Independent Determinant, and R-Squared View the latest post Replies 11 Views 25145
- by Eli 2 weeks ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 72653
-
Intersection of two ideals of a ring R
-
- Member
- Reactions: 1
- Posts: 8
- Joined: 9 years ago
- Been thanked: 1 time
Qn. Show that the intersection of two ideals of a ring R is an ideal
0
- Eli
- Senior Expert Member
- Reactions: 183
- Posts: 5410
- Joined: 9 years ago
- Location: Tanzania
- Has thanked: 75 times
- Been thanked: 88 times
- Contact:
Let me define what is ring and ideal in abstract algebra context.
A ring is a set with two binary operations of and . , such that:
(i) is an abelian group,
(ii) is closed under multiplication and ,
(iii) .
Usually, there is left ideal, right ideal and 2-sided ideal, but, here we mean 2-sided.
A subset of a ring is called an ideal provided it is a subgroup of the additive group and if and then:
(i) ,
(ii) ,
(iii) .
Hope this will give others a highlight and a hint to answer the question!
A ring is a set with two binary operations of and . , such that:
(i) is an abelian group,
(ii) is closed under multiplication and ,
(iii) .
Usually, there is left ideal, right ideal and 2-sided ideal, but, here we mean 2-sided.
A subset of a ring is called an ideal provided it is a subgroup of the additive group and if and then:
(i) ,
(ii) ,
(iii) .
Hope this will give others a highlight and a hint to answer the question!
0
TSSFL -- A Creative Journey Towards Infinite Possibilities!
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests