King Fahd University of Petroleum & Minerals                                                                       Department of Mathematics and Statistics

Commutative Algebra Research Group (CARG)

 
 
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Commutative Algebra “has developed from two sources: (1) Algebraic Geometry and (2) Algebraic Number theory. In (1), the prototype of the rings studied is the ring of polynomials in several variables over a field; in (2), it is the ring of rational integers. Of these two, the algebra-geometric case is the more far-reaching and, in its modern development by Grothendieck, it embraces much of algebraic number theory. Commutative Algebra is now one of the foundation stones of this new algebraic geometry. It provides the complete local tools for the subject in much the same way as differential analysis provides the tools for differential geometry.” [Atiyah - MacDonald, Introduction to Commutative Algebra]

 

The credit for raising Commutative Algebra to a fully-fledged branch of mathematics belongs to many famous mathematicians; including Ernst Kummer (1810-1893), Leopold Kronecker (1823-1891), Richard Dedekind (1831-1916), David Hilbert (1862-1943), Emanuel Lasker (1868-1941), Emmy Noether (1882-1935), Emil Artin (1898-1962), Wolfgang Krull (1899-1971), and Van Der Waerden (1903-1996). Nowadays, Commutative Algebra is rapidly growing and developing in many different directions. It has multiple connections with such diverse fields as complex analysis, topology, homological algebra, algebraic number theory, algebraic geometry, finite fields, and computational algebra.

 

KSA has vast resources along with the potential to become a leader in the region in basic science and mathematics which are the pillars of a knowledge-based society. King Fahd University of Petroleum & Minerals (KFUPM), by virtue of its qualified faculty and infrastructure, can play an important role in this regard.

 

The Commutative Algebra Research Group (CARG), as a University-funded research group, aims at strengthening research and graduate teaching as well as acquiring a national and international reputation for excellence in Commutative Algebra and related fields.