Algebra-Rings, Subrings and Ideals, Homomorphisms of Rings [IAS (Admin.) Mains Mathematics]: Questions 1 - 5 of 5
Choose Programs:
📹 Video Course 2024 (36 Lectures [25 hrs : 50 mins]): Offline Support
Rs. 160.00 -OR-
1 Month Validity (Multiple Devices)
Preview All LecturesDetails
🎓 Study Material (212 Notes): 2024-2025 Syllabus
Rs. 250.00 -OR-
3 Year Validity (Multiple Devices)
Topic-wise Notes & SampleDetails
🎯 668 Questions (& PYQs) with Full Explanations (2024-2025 Exam)
Rs. 1150.00 -OR-
3 Year Validity (Multiple Devices)
CoverageDetailsSample Explanation
Help me Choose & Register (Watch Video) Already Subscribed?
Question 1
Appeared in Year: 2015
Describe in Detail Subjective▾
Give an example of a ring having identity but a subring of this having a different identity. (CS main Paper 2)
EditExplanation
Let and S =
First, we prove R…
… (779 more equations) …
Question 2
Appeared in Year: 2011
Describe in Detail Subjective▾
Let F be the set of all real valued continuous functions defined on the closed interval prove that is a commutative ring with unity with respect to addition and multiplication of function defined point wise as below:
Where (Paper II)
EditExplanation
- Given
T. P…
… (370 more equations) …
Question 3
Appeared in Year: 2013
Describe in Detail Subjective▾
Let of all real valued continuous functions on , under the operations
Let
Is M a maximal ideal of R? Justify your Answer. (Paper II)
EditExplanation
- Define
by
- Let
… (217 more equations) …
Question 4
Appeared in Year: 2014
Describe in Detail Subjective▾
Prove that the set is a commutative ring with identity. (Paper II)
EditExplanation
- Given
- I. is Abelian group
(i) Let
… (600 more equations) …
Question 5
Appeared in Year: 2007
Describe in Detail Subjective▾
Let where . Show that R is a ring under matrix addition and multiplication
Then show that A is a left ideal of R but not a right ideal of R. (Paper II)
EditExplanation
- First, we show that R is a ring under matrix addition and multiplication
I. Is an abelian group
- (a) Closure property:
Let
… (653 more equations) …