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Lecture

Integral Closures: Eisenstein Primes

In course

MATH-311: Algebra IV - rings and modules

Ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra. ...

Description

This lecture covers the concept of integral closures, focusing on Eisenstein primes and their properties. It discusses the integral closure of a domain, internal closure, and examples related to Eisenstein primes.

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Instructors (2)

Zsolt Patakfalvi

See CV here .

Domenico Valloni

Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Related concepts (32)

Domain name

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Top-level domain

A top-level domain (TLD) is one of the domains at the highest level in the hierarchical Domain Name System of the Internet after the root domain. The top-level domain names are installed in the root zone of the name space. For all domains in lower levels, it is the last part of the domain name, that is, the last non empty label of a fully qualified domain name. For example, in the domain name www.example.com, the top-level domain is .com.

Integral element

In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and aj in A such that That is to say, b is a root of a monic polynomial over A. The set of elements of B that are integral over A is called the integral closure of A in B. It is a subring of B containing A. If every element of B is integral over A, then we say that B is integral over A, or equivalently B is an integral extension of A.

Domain name registrar

A domain name registrar is a company that manages the reservation of Internet domain names. A domain name registrar must be accredited by a generic top-level domain (gTLD) registry or a country code top-level domain (ccTLD) registry. A registrar operates in accordance with the guidelines of the designated domain name registries. Until 1999, Network Solutions Inc. (NSI) operated the registries for the com, net, and org top-level domains (TLDs). In addition to the function of domain name registry operator, it was also the sole registrar for these domains.

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