{"id":119,"date":"2022-05-07T05:47:03","date_gmt":"2022-05-07T05:47:03","guid":{"rendered":"https:\/\/src.cikeys.com\/2022\/?page_id=119"},"modified":"2023-02-15T05:24:45","modified_gmt":"2023-02-15T05:24:45","slug":"properties-of-polynomial-rings-over-various-rings-zp-z-r-and-c","status":"publish","type":"page","link":"https:\/\/src.cikeys.com\/2022\/properties-of-polynomial-rings-over-various-rings-zp-z-r-and-c\/","title":{"rendered":"Properties of Polynomial Rings Over Various Rings: Zp, Z, R and C."},"content":{"rendered":"\n

Levi Puga and Dr. Ivona Grzegorczyk<\/h3>\n\n\n\n\n\n\n\n
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Abstract<\/h2>\n\n\n\n

We will analyze and study polynomial rings over Zp, Z, R and C(with one variable). More specifically we will analyze criteria for divisibility, that is, when a polynomial is divisible by another(is a factor) and when a polynomial is irreducible(has \u201cno\u201d roots\/factors). Thanks to certain theorems we can see that polynomials in certain rings will always have roots\/factors and therefore that polynomial will be divisible by that said factor. For instance, due to the Fundamental Theorem of Algebra we can say that a polynomial of degree n will have n roots in the Complex Numbers(C). How about that same polynomial in R? In Z? In Zp? It is also important to see the relationship between being divisible(remainder=0) and having a factor. If a polynomial has a factor then it is divisible by that factor, but not all polynomials will have factors(polynomial is irreducible) We will analyze these questions and more.<\/p>\n<\/div>\n\n\n\n

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Presentation<\/h2>\n\n\n