Reinhold Baer

Reinhold Baer
Born	(1902-07-22)22 July 1902 Berlin, Germany
Died	Zurich, Switzerland
Nationality	German
Fields	Mathematics
Institutions	University of Illinois at Urbana-Champaign Goethe University Frankfurt
Alma mater	University of Göttingen
Doctoral advisor	Hellmuth Kneser
Doctoral students	Bernd Fischer Hermann Heineken Heinrich Lüneburg Gerhard Michler Wolfgang Kappe Grace Bates Kenneth Graham Wolfson

Reinhold Baer (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings and Baer groups.

Biography

Baer studied mechanical engineering for a year at the University of Hanover. He then went to study philosophy at Freiburg in 1921. While he was at Göttingen in 1922 he was influenced by Emmy Noether and Hellmuth Kneser. In 1924 he won a scholarship for specially gifted students. Baer wrote up his doctoral dissertation and it was published in Crelle's Journal in 1927.

Baer accepted a post at Halle in 1928. There, he published Ernst Steinitz's "Algebraische Theorie der Körper" with Helmut Hasse, first published in Crelle's Journal in 1910.

While Baer was with his wife in Austria, Adolf Hitler and the Nazis came into power. Baer was later informed that his services at Halle were no longer required. Louis Mordell invited him to go to Manchester and Baer accepted.

Baer stayed at Princeton University and was a visiting scholar at the nearby Institute for Advanced Study from 1935 to 1937. For a short while he lived in North Carolina. From 1938 to 1956 he worked at the University of Illinois at Urbana-Champaign. He returned to Germany in 1956.

According to biographer K. W. Gruenberg,

The rapid development of lattice theory in the mid-thirties suggested that projective geometry should be viewed as a special kind of lattice, the lattice of all subspaces of a vector space... [Linear Algebra and Projective Geometry (1952)] is an account of the representation of vector spaces over division rings, of projectivities by semi-linear transformations and of dualities by semi-bilinear forms.

Bibliography

• 1934: "Erweiterung von Gruppen und ihren Isomorphismen", Mathematische Zeitschrift 38(1): 375–416 (German) MR 1545456
• 1940: "Nilpotent groups and their generalizations", Transactions of the American Mathematical Society 47: 393–434 MR 0002121
• 1944: "The higher commutator subgroups of a group", Bulletin of the American Mathematical Society 50: 143–160 MR 0009954
• 1945: "Representations of groups as quotient groups. II. Minimal central chains of a group", Transactions of the American Mathematical Society 58: 348–389 MR 0015107
• 1945: "Representations of groups as quotient groups. III. Invariants of classes of related representations", Transactions of the American Mathematical Society 58: 390–419 MR 0015108

See also

• Baer–Suzuki theorem

References

• O. H. Kegel (1979) "Reinhold Baer (1902 — 1979)", Mathematical Intelligencer 2:181,2.

External links

• Erweiterung von Gruppen und ihren Isomorphismen, PDF file
• Reinhold Baer at the Mathematics Genealogy Project
• K.W. Gruenberg & Derek Robinson (2003) The Mathematical Legacy of Reinhold Baer, Illinois Journal of Mathematics 47(1-2) from Project Euclid.
• Author profile in the database zbMATH