Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On rings whose finitely generated left ideals are left annihilators of
  an element   An associative ring $R$ with identity is left pseudo-morphic if for every
$a$$\in$$R$, there exists $b$$\in$$R$ such that $Ra=l_R(b)$. If, in addition,
$l_R(a)=Rb$, then $R$ is called left morphic. $R$ is morphic if it is both left
and right morphic. We characterize left pseudo-morphic rings; identify the
cases a (left) pseudo morphic ring is (left) quasi-morphic, morphic,
Quasi-Frobenius, von Neumann regular, etc.; correct two results in a book and a
paper; and completely determine when the trivial extension of a commutative
domain is morphic which positively answered a question in a paper.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics