Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Positive Zero Divisors in C* Algebras   In this paper we concern with positive zero divisors in $C^{*}$ algebras. By
means of zero divisors, we introduce a hereditary invariant for $C^{*}$
algebras. Using this invariant, we give an example of a $C^{*}$ algebra $A$ and
a $C^{*}$ sub algebra $B$ of $A$ such that there is no a hereditary imbedding
of $B$ into $A$.
  We also introduce a new concept zero divisor real rank of a $C^{*}$ algebra,
as a zero divisor analogy of real rank theory of $C^{*}$ algebras. We observe
that this quantity is zero for $A=C(X)$ when $X$ is a separable compact
Hausdorff space or $X$ is homeomorphic to the unit square with the
lexicographic topology. To a $C^{*}$ algebra $A$ with $\dim A > 1$, we assign
the undirected graph $\Gamma^{+} (A)$ of non zero positive zero divisors. For
the Calkin algebra $A=B(H)/K(H)$, we show that $\Gamma^{+}(A)$ is a connected
graph and diam $\Gamma^{+}(A)= 3$. We show that $\Gamma^{+}(A)$ is a connected
graph with $\text {diam}\; \Gamma^{+}(A)\leq 6$, if $A$ is a factor.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio