Ring Theory|Polynomial ring|Every unit of R is also an unit of R[x]|Lecture 18|Part 4|Theta Classes

In this lecture we are going to discuss another result related to polynomial ring which states that every unit of R is also an unit of R[x]. After understanding this result we will see its proof. And then we learn about whether its converse is also true with the help of an example. 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...   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.