The Importance of Semisimple Artinian Rings - Rowen

[Math Amateur]

In the beginning of his graduate level textbook: Ring Theory, Louis Halle Rowen makes the following statement:

"In the solar system of ring theory the Sun is certainly the semisimple Artinian ring ... ... "Can anyone explain why Rowen might say this?

Do MHB readers agree?

Peter

 

[jvicens]

As a scientist familiar with ring theory, I can provide some insight into why Rowen might make this statement. In ring theory, the term "solar system" is often used to describe a collection of related rings, with the "Sun" representing the most important and fundamental ring in the system. In this case, the Sun is being compared to the semisimple Artinian ring, which is a type of ring that has special properties and is often considered the "simplest" type of ring in the solar system of ring theory.

Rowen may have made this statement to emphasize the importance and centrality of the semisimple Artinian ring in the study of ring theory. Just as the Sun is the center of our solar system and provides light and energy to all the planets, the semisimple Artinian ring plays a crucial role in understanding and building upon more complex rings.

As for whether MHB readers agree, it ultimately depends on their understanding and perspective on ring theory. Some may agree with Rowen's analogy and see the semisimple Artinian ring as the "Sun" of the solar system of ring theory, while others may have a different interpretation. Ultimately, it is up to each individual reader to form their own opinion on the matter.