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Advances in Ring Theory (Trends in Mathematics) by Sergio R. López-Permouth, Dinh Van Huynh

By Sergio R. López-Permouth, Dinh Van Huynh

This quantity includes refereed learn and expository articles by way of either plenary and different audio system on the foreign convention on Algebra and purposes held at Ohio college in June 2008, to honor S.K. Jain on his seventieth birthday. The articles are on a wide selection of components in classical ring thought and module concept, resembling jewelry pleasant polynomial identities, earrings of quotients, workforce jewelry, homological algebra, injectivity and its generalizations, and so forth. incorporated also are functions of ring thought to difficulties in coding idea and in linear algebra.

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Pure Appl. Algebra 206 (2006), 355–369. [7] Y. E. Bell and C. Phipps, On reversible group rings, Bull. Austral. Math. Soc. 74 (2006), 139–142. [8] Y. M. Parmenter, Reversible group rings over commutative rings, Comm. Algebra 35 (2007), 4096–4104. [9] Y. M. Parmenter, Graded reversibility in integral group rings, Acta Appl. Math. 108 (2009), 129–133. [10] G. Marks, Reversible and symmetric rings, J. Pure Appl. Algebra 174 (2002), 311– 318. [11] P. Menal, Group rings in which every left ideal is a right ideal, Proc.

4, we will show that a class C ∈ Skel(R-op) is also closed under extensions and direct sums. The following lemma is proved in [9, Theorem 3]; we include a proof for reader’s convenience. 7. Each D ∈ Skel(R-op) is closed under extensions and direct sums. Proof. Suppose D = C⊥{≤, . f g Extensions. Let 0 → L → M → N → 0 be an exact sequence with L, N ⊥{≤, } ∈C . To show a contradiction, suppose that 0 = K ∈ C is a subquotient of M, as in the diagram M ↓α , β K C where α is epic and β is monic. As β (K) ∩ αf (L) is a subquotient of both L and K, then β (K) ∩ αf (L) = 0.

Pure Appl. Algebra 209 (2007), 833–838. P. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), 641–648. [4] W. Gao and Y. Li, On duo group rings, Algebra Colloq. In press, 2008. [5] M. Gutan and A. Kisielewicz, Reversible group rings, J. Algebra 279 (2004), 280–291. [6] M. Gutan and A. Kisielewicz, Rings and semigroups with permutable zero products, J. Pure Appl. Algebra 206 (2006), 355–369. [7] Y. E. Bell and C. Phipps, On reversible group rings, Bull. Austral. Math. Soc. 74 (2006), 139–142.

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