A principal ideal ring (PIR) may have zero divisors unlike a principal ideal domain(PID). For example: Quotient Ring Z/(4Z) is a PIR . Infact every Quotient Ring of a PID is a PIR. In this example, Z, the set of all integers, is a PID and thus has no zero divisors while its Quotient Ring Z/(4Z) does have zero divisor in the form of element 2+(4Z).
For an ideal of a ring R to be a principal ideal it is not necessary that R will be a ring with unity. I thik 2Z also have a principal ideal . In fact 2Z is also a principal ideal ring
Let Sl and S2 be any two ideals of R, then the ideal generated by S 1 US 2 is the set S1+ S2 obtained by adding each element of Sl with each element of S2 .? Please answer this question
Following u from my BSc first year and now I am in MSc still following u ..u r fabulous
The way you explained it is really amazing,,,,,, Thanks from Bangladesh
Really the best i have ever seen such a teaching mam
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Thank you ma'am , aap bhut hi saralata se in kathin chizo ko smjha leti ho🤗
Superb Mam👍👍👍👍👍
A principal ideal ring (PIR) may have zero divisors unlike a principal ideal domain(PID). For example: Quotient Ring Z/(4Z) is a PIR . Infact every Quotient Ring of a PID is a PIR. In this example, Z, the set of all integers, is a PID and thus has no zero divisors while its Quotient Ring Z/(4Z) does have zero divisor in the form of element 2+(4Z).
Very helpful video pls make more video and cover all imp theorm and question tnku so much mam
Hlo mam plz upload ba final year all maths videos.... Ur videos are very helpful.... Bhut acha pdhate ho mam ap🙏
For an ideal of a ring R to be a principal ideal it is not necessary that R will be a ring with unity. I thik 2Z also have a principal ideal . In fact 2Z is also a principal ideal ring
Mam can u make vedios on permutation groups and conjugate elements plz 🙏🙏🙏 yours vedios very helpful
Achcha tarika
can help me
Given that (l,+,.) is an ideal of the ring (R,+,.) Show that: if (R,+,.) is a principal ideal ring ,then so is the quotient ring (R/l,+,.)
Let Sl and S2 be any two ideals of R, then the ideal generated by S 1 US 2 is the set S1+ S2 obtained by adding each element of Sl with each element of S2 .?
Please answer this question
very nice
Thanku mam🥰😊
Tanks mam video banane ke lie
Mam. Sylows theorem application of ring theory. How to check in sylows theorem in ring
Mam plz module theory pe videos bnaeye
mam Euclidean ring krwa do please
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Thanks mam.
Didi statics ka force of friction chapter revise krwa do plz
Thanks beauty ravina
All theory portion is waste if you have not any kinds of example .
Here everything is wrong
Bakwas