Ring Theory|If R is an integral domain then U(R)=U(R[x])|Lecture 18|Part 5|Polynomial ring

This lecture is the continuation of previous result in which we had discussed that under what condition will units of ring R and polynomial ring R[x] are same. So this lecture answer this question in the form of result 5 in which we learn that when R is an integral domain then units will be same. After that we will discuss its proof also and in order to have better understanding we will find units of polynomial ring using this result. Lecture 1 on ring defintion    • Ring Theory|Definition of ring|Examples of...   Lecture 2 on types of ring:    • Ring Theory|Commutative ring|Ring with uni...   Lecture 3 on example of commutative ring with unity    • Ring Theory|Commutative ring with unity ex...   Lecture 4 on Z[i] is a CRU    • Ring Theory|Set of gaussian integer is a c...   Lecture 5 on examples of ring:    • Ring Theory|Commutative ring|Commutative r...   Lecture 6 on examples of ring:    • Ring Theory| Set of all real valued contin...   Lecture 7 on properties of ring:    • Ring Theory|Properties of rings|CSIR NET|G...   Lecture 8 on zero divisor:    • Ring Theory|Zero divisor|Ring with zero di...   Lecture 9 on integral domain    • Ring Theory|Integral Domain|Integral domai...   Lecture 10 on units of a ring    • Ring Theory|Units in a ring|Number of unit...   Lecture 11 on field    • Ring Theory|Definition of Field|17 example...   Lecture 12 on Every field is an integral domain    • Ring Theory|Every field is an integral dom...   Lecture 13 on every finite integral domain is a field    • Ring Theory|Every finite integral domain i...   Lecture 14 on division ring or skew field    • Ring Theory|Division ring|Skew field|Divis...   Lecture 15 on properties of division ring    • Ring Theory|A division ring has no zero di...   Lecture 16 on polynomial ring    • Ring Theory|Polynomial ring|Definition|Exa...   Lecture 17 on degree of polynomials    • Ring Theory|Polynomial ring|Degree of a po...   Lecture 18 on results on polynomial ring    • Ring Theory|Polynomial ring|Results on pol...   Polynomial ring over integral domain    • Ring Theory|Polynomial ring|Polynomial rin...   Polynomial ring not a field    • Ring Theory|Polynomial ring|Polynomial rin...   Every unit of R is also an unit of R[x]    • Ring Theory|Polynomial ring|Every unit of ...   In case if any student finds any difficulty in understanding this lecture do mention it in comment section. Keep connected with @thetaclasses to study various topics of higher mathematics. Thank you and love you all.