Summary of Ring Theory 1: Ring Definition and Examples

00:00:00 - 00:15:00

This video introduces the concept of a ring and provides examples of how it can be used in mathematics. A ring is a set of objects that share a common mathematical operation, such as addition or multiplication. A ring can be commutative or not commutative, and may have a multiplicative identity or not. Rings can be simpler or more complex, and are used in various fields of mathematics.

• 00:00:00 In this video, a set of conditions is given for a ring, and it is shown that the set satisfies these conditions. Additionally, the existence of an identity and additive inverse for the ring are mentioned. Finally, the ring is shown to be associative under multiplication and addition.
• 00:05:00 In this video, Ring Theory is introduced, and the Ring Theory concept of a ring is defined. The Ring Theory property of being associative and closed under multiplication is shown to hold for the integers. An example of a ring is then given, involving disease. Finally, other examples of rings are given, and the Ring Theory property of distributivity is shown to hold for all of them.
• 00:10:00 In this video, Murray explains the concept of a ring and its various components. A ring is a set of objects that share a common mathematical operation, such as addition or multiplication. A ring can be commutative or not commutative, and may have a multiplicative identity or not. Rings can be simpler or more complex, and are used in various fields of mathematics.
• 00:15:00 This video explains the concept of rings, including the definition and examples of a ring with unity, as well as the concept of multiplicative inverses. It also provides practice problems to help you understand the concept.