Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anticommutativity of Skew-symmetric Elements under Generalized Oriented
  Involutions   Let $R$ be a ring with $char(R)\neq2$ whose unit group are denoted by
$\mathcal{U}(R)$, $G$ a group, and $RG$ its group ring. Let $*$ be an
involution in $G$, $\sigma:G\rightarrow\mathcal{U}(R)$ be a nontrivial group
homomorphism, with $ker\ \sigma=N$, satisfying $xx^*\in N$ for all $x\in G$,
and define the generalized oriented involution $\sigma*$ in $RG$ by $\left(
\sum_{x\in G}\alpha_xx\right)^{\sigma*}=\sum_{x\in G}\sigma(x)\alpha_xx^*$. An
element $\alpha\in RG$ is called skew-symmetric if $\alpha^{\sigma *}=-\alpha$,
and the set of all skew-symmetric elements are denoted by $(RG)^-$. In this
paper, we will classify the group rings $RG$ such that $(RG)^-$ is
anticommutative, generalizing, and obtaining as consequence, the main result of
\cite{GP13a}.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics