Transactions of the American Mathematical Society, Vol. 299, No. 1 (Jan., 1987), pp. 373-386 (14 pages) It is proven that the group ring of an amalgamated free product of residually torsion free ...
Transactions of the American Mathematical Society, Vol. 288, No. 2 (Apr., 1985), pp. 605-623 (19 pages) Let k be a field, and let G be a countable nilpotent group with centre Z. We show that the group ...
The original version of this story appeared in Quanta Magazine. Mathematics started with numbers—clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract ...
Description: Review of fundamental structures of algebra (groups, rings, fields, modules, algebras): Jordan-Hlder and Sylow theorems; Galois theory; bilinear forms; modules over principal ideal ...
Algebraic structures form the backbone of modern abstract algebra, encapsulating a wide range of systems such as groups, rings, fields, and modules, each characterised by distinct axiomatic properties ...
What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question. Mathematics started with numbers — clear, ...
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