Ring Theory|Every finite integral domain is a field|Proof|Lecture 13|CSIR NET|GATE|Theta Classes

In this lecture we are going to learn and prove that every finite integral domain is a field. For this we will first recall the previous lecture which states that every field is an integral domain but its converse part not true. So connecting with this we state that if finitness condition is being applied on integral domain then its converse is true. With this we define the statement that states every finite integral domain is a field. After that we prove the above statement. Link for lecture 1 on ring defintion    • Ring Theory|Definition of ring|Examples of...   Link for lecture 2 on types of ring:    • Ring Theory|Commutative ring|Ring with uni...   Link for lecture 3 on example of commutative ring with unity    • Ring Theory|Commutative ring with unity ex...   Link for lecture 4 on Z[i] is a CRU    • Ring Theory|Set of gaussian integer is a c...   Link for lecture 5 on examples of ring:    • Ring Theory|Commutative ring|Commutative r...   Link for lecture 6 on examples of ring:    • Ring Theory| Set of all real valued contin...   Link for lecture 7 on properties of ring:    • Ring Theory|Properties of rings|CSIR NET|G...   Link for lecture 8 on zero divisor:    • Ring Theory|Zero divisor|Ring with zero di...   Link for lecture 9 on integral domain    • Ring Theory|Integral Domain|Integral domai...   Link for 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...   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.