- #1
roger
- 318
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whats a ring ?
What is a Cartesian Product of R with Itself?
- Context: Undergrad
- Thread starter roger
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- Ring
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Discussion Overview
The discussion revolves around the concept of a Cartesian product, specifically the Cartesian product of the set of real numbers (R) with itself. Participants explore the relevance of this concept in the context of abstract algebra and its applications in theoretical physics.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Homework-related
Main Points Raised
- One participant inquires about the definition of a ring, indicating a lack of understanding of the concept.
- Another participant provides a link to a resource on rings, suggesting it is useful for understanding the topic.
- There is a mention of the relevance of rings to theoretical physics, with one participant asserting that abstract algebra is frequently used in this field.
- A participant expresses confusion about the notation R^2 and its connection to a previous discussion involving double integrals.
- One participant explains that R^2 refers to the Cartesian product of R with itself, implying a foundational understanding of Cartesian products is necessary.
- Another participant suggests that introductory abstract algebra should be studied in high school or college for better comprehension of rings and related concepts.
Areas of Agreement / Disagreement
Participants express varying levels of understanding regarding rings and their applications. There is no consensus on the clarity of the concept of a Cartesian product or its relevance to physics, as some participants seek further clarification while others assert its importance.
Contextual Notes
Some participants express confusion about specific mathematical notations and concepts, indicating potential gaps in foundational knowledge. The discussion does not resolve these uncertainties.
Who May Find This Useful
Readers interested in abstract algebra, mathematical structures, and their applications in physics may find this discussion relevant.
- #2
dextercioby
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- #3
roger
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dextercioby said:
yes, i also looked at that site too.. but I don't understand it all.
What did you mean by r^2 by the way ?
and do rings have relevance to physics ??
- #4
dextercioby
Science Advisor
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I didn't see any [itex]r^{2}[/itex]...
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
- #5
Vanes63
- 8
- 0
Abstract Algebra
Take a set, give it a few properties, that's what most of abstract algebra is about.
A ring is just one of the structures that is studied in abstract/modern algebra.
Start with groups, then it will get you to identify what a ring is a little better.
- Vanes.
Take a set, give it a few properties, that's what most of abstract algebra is about.
A ring is just one of the structures that is studied in abstract/modern algebra.
Start with groups, then it will get you to identify what a ring is a little better.
- Vanes.
- #6
roger
- 318
- 0
dextercioby said:I didn't see any [itex]r^{2}[/itex]...
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
How do you get started studying rings though ?
I wanted to know what you meant by R^2 when you showed me the double integral..in the other homework question.
- #7
dextercioby
Science Advisor
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Aaaaa,got it.You've studied cartesian (direct) product.It's the cartesian product of R with itself.
You should have introductory abstract algebra in high-school.If not,then definitely in college,if u take a math major.
Daniel.
You should have introductory abstract algebra in high-school.If not,then definitely in college,if u take a math major.
Daniel.
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