How Long to Read Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains

How Long Does it Take to Read Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains?

It takes the average reader 1 hour and 41 minutes to read Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains by Valentina Barucci

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Description

If $k$ is a field, $T$ an analytic indeterminate over $k$, and $n_1, \ldots , n_h$ are natural numbers, then the semigroup ring $A = k[[T^{n_1}, \ldots , T^{n_h}]]$ is a Noetherian local one-dimensional domain whose integral closure, $k[[T]]$, is a finitely generated $A$-module. There is clearly a close connection between $A$ and the numerical semigroup generated by $n_1, \ldots , n_h$. More generally, let $A$ be a Noetherian local domain which is analytically irreducible and one-dimensional (equivalently, whose integral closure $V$ is a DVR and a finitely generated $A$-module). As noted by Kunz in 1970, some algebraic properties of $A$ such as ``Gorenstein'' can be characterized by using the numerical semigroup of $A$ (i.e., the subset of $N$ consisting of all the images of nonzero elements of $A$ under the valuation associated to $V$ ). This book's main purpose is to deepen the semigroup-theoretic approach in studying rings A of the above kind, thereby enlarging the class of applications well beyond semigroup rings. For this reason, Chapter I is devoted to introducing several new semigroup-theoretic properties which are analogous to various classical ring-theoretic concepts. Then, in Chapter II, the earlier material is applied in systematically studying rings $A$ of the above type. As the authors examine the connections between semigroup-theoretic properties and the correspondingly named ring-theoretic properties, there are some perfect characterizations (symmetric $\Leftrightarrow$ Gorenstein; pseudo-symmetric $\Leftrightarrow$ Kunz, a new class of domains of Cohen-Macaulay type 2). However, some of the semigroup properties (such as ``Arf'' and ``maximal embedding dimension'') do not, by themselves, characterize the corresponding ring properties. To forge such characterizations, one also needs to compare the semigroup- and ring-theoretic notions of ``type''. For this reason, the book introduces and extensively uses ``type sequences'' in both the semigroup and the ring contexts.

How long is Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains?

Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains by Valentina Barucci is 98 pages long, and a total of 25,284 words.

This makes it 33% the length of the average book. It also has 31% more words than the average book.

How Long Does it Take to Read Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 18 minutes to read Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains aloud.

What Reading Level is Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains?

Maximality Properties in Numerical Semigroups and Applications to One-dimensional Analytically Irreducible Local Domains is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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