mathematics

Maurice Auslander

Maurice Auslander 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 Maurice Auslander rather than just read about it. In short: Maurice Auslander (August 3, 1926 – November 18, 1994) was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras (e.g. finite-dimensional associative algebras over a field). He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Ausl…

Key takeaways

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

Reference excerpt

Maurice Auslander (August 3, 1926 – November 18, 1994) was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras (e.g. finite-dimensional associative algebras over a field). He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras. Born in Brooklyn, New York, Auslander received his bachelor's degree and his Ph.D. (1954) from Columbia University. He was a visiting scholar at the Institute for Advanced Study in 1956-57. He was a professor at Brandeis University from 1957 until his death in Trondheim, Norway, aged 68. He was elected a Fellow of the American Academy of Arts and Sciences in 1971. Auslander was married to Bernice Auslander, a professor emerita of mathematics at University of Massachusetts at Boston. He had two children. His son Philip Auslander became a professor in the School of Literature, Media, and Communication at Georgia Tech, and his daughter Leora Auslander became a professor of history at the University of Chicago. Maurice Auslander's brother Louis Auslander was also a mathematician.

Selected publications

Articles with David Buchsbaum: Homological dimension in Noetherian rings, Trans. Amer. Math. Soc., vol. 85, 1957, pp. 390–405 doi:10.2307/1992937 with Oscar Goldman: The Brauer group of a commutative ring, Trans. Amer. Math. Soc., vol. 97, no. 3, 1960, pp. 367–409 doi:10.2307/1993378 Modules over unramified regular local rings, Illinois J. Math., vol. 5, 1961, pp. 631–647 with Idun Reiten: Representation theory of Artin algebras. III. Almost split sequences, Communications in Algebra, vol. 3, 1975, pp. 239–294 doi:10.1080/00927877508822046 with Idun Reiten: On a generalized version of the Nakayama conjecture, Proc. Amer. Math. Soc., vol. 52, 1975, pp. 69–74 doi:10.1090/S0002-9939-1975-0389977-6

Books with Mark Bridger: Stable module theory, American Mathematical Society 1969 with David Buchsbaum: Groups, rings, modules, Harper and Row 1974; Auslander, Maurice; Buchsbaum, David (2014). Dover reprint. Courier Corporation. ISBN 978-0-486-49082-3. with Idun Reiten and Sverre O. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, 1995 ISBN 0-521-41134-3

References Notes

Sources Auslander, Maurice (1999), Reiten, Idun; Smalø, Sverre O.; Solberg, Øyvind (eds.), Selected works of Maurice Auslander. Part 1, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0998-3, MR 1674397 Auslander, Maurice (1999), Reiten, Idun; Smalø, Sverre O.; Solberg, Øyvind (eds.), Selected works of Maurice Auslander. Part 2, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1000-2, MR 1674401 Peskine, Christian; Reiten, Idun (1995), "Maurice Auslander (1926–1994)" (PDF), Notices of the American Mathematical Society, 42 (4): 450–453, ISSN 0002-9920, MR 1319276

External links Maurice Auslander Distinguished Lectures Maurice Auslander, Mathematician, 68, New York Times obituary O'Connor, John J.; Robertson, Edmund F., "Maurice Auslander", MacTutor History of Mathematics Archive, University of St Andrews Maurice Auslander at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Maurice Auslander

Start with the simplest possible case. Write down what Maurice Auslander 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 Maurice Auslander 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 Maurice Auslander 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 Maurice Auslander

In research: Maurice Auslander 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 Maurice Auslander 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: Maurice Auslander is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1926 births, 1994 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Maurice Auslander 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 Maurice Auslander in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Maurice Auslander 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 Maurice Auslander out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Maurice Auslander in simple terms?

Why does Maurice Auslander 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 Maurice Auslander?

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 Maurice Auslander.