Alfred Leon Foster (1904-1994) was an American mathematician.Alfred L. Foster, U. of California: In Memoriam, 1995
/ref> He was a professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, from 1934 until 1971. In 1932, he was an Invited Speaker at the ICM in Zürich. In 1934, he accepted a regular position at

Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California *George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer to ...

. At that time, Griffith Evans was Head of the Mathematics Department and was charged by President Sproul with building a first-class mathematics center, which he did. Alfred Foster and

Charles Morrey Charles Bradfield Morrey Jr. (July 23, 1907 – April 29, 1984) was an American mathematician who made fundamental contributions to the calculus of variations and the theory of partial differential equations. Life Charles Bradfield Morrey Jr. ...

(the first department chairman after Evans' retirement) were Evans' first two appointments. Except for subsequent sabbatical leaves, spent most notably in

Freiburg Freiburg im Breisgau or simply Freiburg is the List of cities in Baden-Württemberg by population, fourth-largest city of the German state of Baden-Württemberg after Stuttgart, Mannheim and Karlsruhe. Its built-up area has a population of abou ...

and

Tübingen Tübingen (; ) is a traditional college town, university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer (Neckar), Ammer rivers. about one in ...

, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971. Foster's Ph.D. dissertation and his first few papers were in

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

. From this point, he soon focused on the related theory of

Boolean algebras In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a gene ...

and

Boolean rings In mathematics, a Boolean ring is a ring for which for all in , that is, a ring that consists of only idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplicati ...

and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory. Subsequently, he developed a theory of n-ality for certain rings, which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research. This work culminated in his seminal paper "The Theory of Boolean-like Rings", appearing in 1946. Foster was married to Else Wagner; their marriage produced four children and eight grandchildren.

Selected publications

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References

20th-century American mathematicians University of California, Berkeley College of Letters and Science faculty Princeton University alumni 1904 births 1994 deaths California Institute of Technology alumni {{Mathematician-stub