{"product_id":"9780792371878","title":"Serial Rings","description":"\u003ch1\u003eSerial Rings\u003c\/h1\u003e \u003ch2\u003ePuninski, G.\u003c\/h2\u003e \u003cp\u003eThe main theme in classical ring theory is the structure theory of rings of a particular kind. For example, no one text book in ring theory could miss the Wedderburn-Artin theorem, which says that a ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of full matrix rings over skew fields. This is an example of a finiteness condition which, at least historically, has dominated in ring theory. Ifwe would like to consider a requirement of a lattice-theoretical type, other than being Artinian or Noetherian, the most natural is uni-seriality. Here a module M is called uni-serial if its lattice of submodules is a chain, and a ring R is uni-serial if both RR and RR are uni-serial modules. The class of uni-serial rings includes commutative valuation rings and closed under homomorphic images. But it is not closed under direct sums nor with respect to Morita equivalence: a matrix ring over a uni-serial ring is not uni-serial. There is a class of rings which is very close to uni-serial but closed under the constructions just mentioned: serial rings. A ring R is called serial if RR and RR is a direct sum (necessarily finite) of uni-serial modules. Amongst others this class includes triangular matrix rings over a skew field. Also if F is a finite field of characteristic p and G is a finite group with a cyclic normal p-Sylow subgroup, then the group ring FG is serial.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2001-08-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792371878\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-010-0652-1\u003c\/p\u003e \u003cp\u003eDimensions: 244cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 226\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46544941514892,"sku":"9780792371878","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792371878_2122eb5a-381d-4e1f-bd9d-4cd13634d260.jpg?v=1775756769","url":"https:\/\/lateknightbooks.com\/products\/9780792371878","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}