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cp4space.hatsya.com | ||
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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mattbaker.blog
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| | | | | In my previous post, I presented a proof of the existence portion of the structure theorem for finitely generated modules over a PID based on the Smith Normal Form of a matrix. In this post, I'd like to explain how the uniqueness portion of that theorem is actually a special case of a more general... | |
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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vitalyobukhov.wordpress.com
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| | | Visit the post for more. | ||
