G. Puninski's Serial Rings PDF

By G. Puninski

ISBN-10: 0792371879

ISBN-13: 9780792371878

ISBN-10: 9401038627

ISBN-13: 9789401038621

the most subject in classical ring idea is the constitution thought of jewelry of a specific sort. for instance, nobody textual content publication in ring thought may well leave out the Wedderburn-Artin theorem, which says ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of complete matrix jewelry over skew fields. this is often an instance of a finiteness situation which, not less than traditionally, has ruled in ring thought. Ifwe want to reflect on a demand of a lattice-theoretical variety, except being Artinian or Noetherian, the main average is uni-seriality. the following a module M is termed uni-serial if its lattice of submodules is a sequence, and a hoop R is uni-serial if either RR and RR are uni-serial modules. the category of uni-serial earrings comprises commutative valuation jewelry and closed less than homomorphic photographs. however it isn't closed below direct sums nor with admire to Morita equivalence: a matrix ring over a uni-serial ring isn't uni-serial. there's a category of earrings that's very on the subject of uni-serial yet closed lower than the buildings simply pointed out: serial earrings. a hoop R is termed serial if RR and RR is an instantaneous sum (necessarily finite) of uni-serial modules. among others this category comprises triangular matrix jewelry over a skew box. additionally if F is a finite box of attribute p and G is a finite team with a cyclic general p-Sylow subgroup, then the crowd ring FG is serial.

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Serial Rings by G. Puninski

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