mathematics

Wolfgang Krull

Wolfgang Krull is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Wolfgang Krull rather than just read about it. In short: Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden.

Key takeaways

Wolfgang Krull belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Wolfgang Krull to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Wolfgang Krull from memory before moving on to harder problems.

Reference excerpt

Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden. He attended the Universities of Freiburg, Rostock and finally Göttingen from 1919–1921, where he earned his doctorate under Alfred Loewy. He worked as an instructor and professor at Freiburg, then spent a decade at the University of Erlangen. In 1939, Krull moved to become chair at the University of Bonn, where he remained for the rest of his life. Wolfgang Krull was a member of the Nazi Party. His 35 doctoral students include Wilfried Brauer, Karl-Otto Stöhr and Jürgen Neukirch.

See also Cohen structure theorem Jacobson ring Local ring Prime ideal Real algebraic geometry Regular local ring Valuation ring Krull dimension Krull ring Krull topology Krull–Azumaya theorem Krull–Schmidt category Krull–Schmidt theorem Krull's intersection theorem Krull's principal ideal theorem Krull's separation lemma Krull's theorem

Publications Krull, Wolfgang (1935), Idealtheorie, Ergebnisse der Mathematik, Springer Krull, Wolfgang (1999), Ribenboim, Paulo (ed.), Gesammelte Abhandlungen/Collected papers. Vol. 1, 2 (in German), Berlin: Walter de Gruyter & Co., ISBN 978-3-11-012771-3, MR 1711477

References

External links

O'Connor, John J.; Robertson, Edmund F., "Wolfgang Krull", MacTutor History of Mathematics Archive, University of St Andrews Wolfgang Krull at the Mathematics Genealogy Project

Illustrations

Wolfgang Krull: Wolfgang Krull, Göttingen 1920 — Wolfgang Krull, Göttingen 1920

Worked examples

Example 1 — a first encounter with Wolfgang Krull

Start with the simplest possible case. Write down what Wolfgang Krull claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Wolfgang Krull before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Wolfgang Krull ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Wolfgang Krull

In research: Wolfgang Krull appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Wolfgang Krull in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Wolfgang Krull is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1899 births, 1971 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Wolfgang Krull outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Wolfgang Krull in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wolfgang Krull means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Wolfgang Krull out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wolfgang Krull in simple terms?

Why does Wolfgang Krull matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Wolfgang Krull?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Wolfgang Krull.