By Tomasz Brzezinski, José Luis Gomez-Pardo, Ivan Shestakov, Patrick F. Smith

ISBN-10: 3764387416

ISBN-13: 9783764387419

ISBN-10: 3764387424

ISBN-13: 9783764387426

The 23 articles during this quantity surround the lawsuits of the foreign convention on Modules and Comodules held in Porto (Portugal) in 2006 and devoted to Robert Wisbauer at the social gathering of his sixty fifth birthday. those articles replicate Professor Wisbauer's large pursuits and provides an outline of other fields with regards to module concept, a few of that have an extended culture while others have emerged in recent times. They contain subject matters within the formal concept of modules bordering on type conception, in ring conception, in Hopf algebras and quantum teams, and in corings and comodules.

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**Extra info for Modules and Comodules (Trends in Mathematics)**

**Example text**

Algebra 170(2) (1994), 400–421. K. Nauman, Morita similar matrix rings and their Grothendieck groups, Aligarh Bull. Math. 23(1-2) (2004), 49–60. [Sat1978] M. Sato, Fuller’s Theorem of equivalences, J. Algebra 52 (1978), 274–284. [Tak1977] M. Takeuchi, Morita theorems for categories of comodules, J. Fac. Univ. Tokyo 24 (1977), 629–644. [Trl1994] J. Trlifaj, Every ∗-module is ﬁnitely generated, J. Algebra 169 (1994), 392–398. [Ver2006] J. Vercruysse, Local units versus local dualisations: corings with local structure maps, Commun.

Let ((Xi )i∈N , (ξij )i,j∈N ) be a direct system in M where, for i ≤ j, ξij : Xi → Xj . Let (ξi : Xi → X)i∈N be a compatible family of morphisms with respect to the given direct system. Fix n ∈ N and assume that • ξii+1 : Xi → Xi+1 is a split monomorphism for every 0 ≤ i ≤ n − 1, • X0 = 0, • there exists λn : X → Xn such that λn ◦ ξj = ξjn , for every j ≤ n and denote by τi : X → X Xi (18) the canonical projection for every i ∈ N. Then the following sequence is exact. Xa ⊗ Xb ∇[(ξa ⊗ξb )a+b=n+1 ] −→ X ⊗X ∆[(τa ⊗τb )a+b=n ] −→ a+b=n+1 a+b=n X X ⊗ .

Tak1977] M. Takeuchi, Morita theorems for categories of comodules, J. Fac. Univ. Tokyo 24 (1977), 629–644. [Trl1994] J. Trlifaj, Every ∗-module is ﬁnitely generated, J. Algebra 169 (1994), 392–398. [Ver2006] J. Vercruysse, Local units versus local dualisations: corings with local structure maps, Commun. Algebra 34 (2006), 2079–2103. [Wis1991] R. Wisbauer, Foundations of Module and Ring Theory, a Handbook for Study and Research, Gordon and Breach Science Publishers (1991). Y. K. Nauman [Wis1998] R.

### Modules and Comodules (Trends in Mathematics) by Tomasz Brzezinski, José Luis Gomez-Pardo, Ivan Shestakov, Patrick F. Smith

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