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A question about Group Rings

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#abstract-algebra #ring-theory #group-rings
513
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The division algebras arising in the Wedderburn decomposition of a finite group modulo its radical in characteristic $p$

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#group-theory #finite-groups #representation-theory #group-rings
220
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Are augmented algebra maps of group algebras group homomorphisms?

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#abstract-algebra #group-theory #finite-groups #group-rings
99
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group algebra and kernel

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#abstract-algebra #group-rings
1k
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Projective modules over $kG$ equivalent to injective.

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#abstract-algebra #homological-algebra #projective-module #injective-module #group-rings
99
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Embedding the base ring in the augmentation ideal of a group algebra

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#abstract-algebra #ring-theory #group-rings
232
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Is the coefficient ring $R$ of a group ring $RG$ necessarily projective as an $RG$-module?

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#representation-theory #projective-module #group-rings
216
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Identities of a group ring

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#abstract-algebra #group-rings
267
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Consider $\mathbf{Z}G$, $G$ finite. If the characters of two $\mathbf{Z}G$-modules are equal, does it follow that the modules are isomorphic?

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#representation-theory #modules #characters #group-rings
299
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Is the Transpose of a Representation an Equivalent Representation?

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#representation-theory #characters #group-rings
513
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Jacobson radical of the integral group ring

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#representation-theory #group-rings
379
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Rational group algebras and maximal orders

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#abstract-algebra #commutative-algebra #abelian-groups #cyclic-groups #group-rings
369
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Can the integral group ring construction be extended to groupoids in such a way that it provides a functor from Groupoids to Rings?

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#abstract-algebra #category-theory #modules #group-rings #groupoids
1.2k
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Is the quotient of a torsion-free module torsion-free?

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#group-rings #torsion-groups
96
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Is $R\otimes_R M\cong M$ when $R$ not necessarily commutative?

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#modules #tensor-products #group-rings

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