By Lopez-Permouth S., Huynh D.V. (eds.)

ISBN-10: 3034602855

ISBN-13: 9783034602853

This quantity comprises refereed examine and expository articles by means of either plenary and different audio system on the overseas convention on Algebra and functions held at Ohio collage 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 idea, akin to jewelry pleasurable polynomial identities, jewelry of quotients, workforce earrings, homological algebra, injectivity and its generalizations, and so on. incorporated also are purposes of ring thought to difficulties in coding concept and in linear algebra.

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A. Rinc´ on Mej´ıa and J. R´ıos Montes Now, if C ≤ D ∈ LQ, then D = E ⊥P , for some E ∈ LP , by hypothesis. Then C ≤ ≤ D⊥P ⊥P = E ⊥P ⊥P ⊥P = E ⊥P = D, this shows that C ⊥P ⊥P = LQ (C). 1. 4 we notice that the skeletons of R-tors, (which is L{≤, ,ext,⊕} ), of R-Serre (which is L{≤, ,ext} ) and of R-op (which is L{≤, } ) are all the same. 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.

Duo group algebras As mentioned earlier, if a group ring RG over a commutative ring is duo, then it is reversible. 8). A natural question which arises is whether a reversible group algebra KG is also duo. An aﬃrmative answer was given by Bell and the Li in [2]. The following result proved in [2] characterizes when a group algebra KQ8 is duo. 4. The following statements are equivalent: (1) KQ8 is duo. (2) The equation 1 + x2 + y 2 = 0 has no solutions in K when char(K) = 2, or the equation 1 + x + x2 = 0 has no solutions in K when char(K) = 2.

Algebra 29(2001), no. 1, 131–140. [15] Raggi, Francisco, R´ıos Montes, Jos´e, Wisbauer, Robert, Coprime preradicals and modules. J. Pure Appl. Algebra 200 (2005), no. 1-2, 51–69. , Serre subcategories of R-mod. Comm. Algebra 24 (1996), no. 9, 2877–2886. [17] R. Bronowitz and M. Teply, Torsion theories of simple type, J. Pure Appl. Algebra 3 (1973), 329–336. [18] B. Stenstr¨ om, Rings of Quotients, Springer-Verlag, New York, 1975. [19] Y. Zhou, The Lattice of natural classes of modules, Comm. Algebra 24 (5) (1996) 1637–1648.

### Advances in ring theory by Lopez-Permouth S., Huynh D.V. (eds.)

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