Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prime M-Ideals, M-Prime Submodules, M-Prime Radical and M-Baer's Lower
  Nilradical of Modules   Let M be a fixed left R-module. For a left R-module X, we introduce the
notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R,
which coincides with prime (resp. semiprime) submodule of X. Other concepts
encountered in the general theory are M-m-system sets, M-n-system sets, M-prime
radical and M-Baer's lower nilradical of modules. Relationships between these
concepts and basic properties are established. In particular, we identify
certain submodules of M, called "prime M-ideals", that play a role analogous to
that of prime (two-sided) ideals in the ring R. Using this definition, we show
that if M satisfes condition H (defined latter) and Hom_R(M,X)\neq 0$ for all
modules X in the category \sigma[M], then there is a one-to-one correspondence
between isomorphism classes of indecomposable M-injective modules in \sigma[M]
and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime
submodules and M-prime radical of Artinian modules.

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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: ao-sci