15A63 Quadratic and bilinear forms, inner products [See mainly <a href="#code:11Exx">11Exx</a>]

15A69 Multilinear algebra, tensor products

15A72 Vector and tensor algebra, theory of invariants [See also <a href="#code:13A50">13A50</a>, <a href="#code:14L24">14L24</a>]

15A75 Exterior algebra, Grassmann algebras

15B05 Toeplitz, Cauchy, and related matrices

15B33 Matrices over special rings (quaternions, finite fields, etc.)

15B36 Matrices of integers [See also <a href="#code:11C20">11C20</a>]

15B48 Positive matrices and their generalizations; cones of matrices

15B57 Hermitian, skew-Hermitian, and related matrices

15B99 None of the above, but in this section

16-XX Associative rings and algebras {For the commutative case, see <a href="#code:13-XX">13-XX</a>}

16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

16-01 Instructional exposition (textbooks, tutorial papers, etc.)

16-02 Research exposition (monographs, survey articles)

16-03 Historical (must also be assigned at least one classification number from Section 01)

16-04 Explicit machine computation and programs (not the theory of computation or programming)

16-06 Proceedings, conferences, collections, etc.

16B50 Category-theoretic methods and results (except as in <a href="#code:16D90">16D90</a>) [See also <a href="#code:18-XX">18-XX</a>]

16B70 Applications of logic [See also <a href="#code:03Cxx">03Cxx</a>]

16B99 None of the above, but in this section

16D30 Infinite-dimensional simple rings (except as in <a href="#code:16Kxx">16Kxx</a>)

16D40 Free, projective, and flat modules and ideals [See also <a href="#code:19A13">19A13</a>]

16D50 Injective modules, self-injective rings [See also <a href="#code:16L60">16L60</a>]

16D60 Simple and semisimple modules, primitive rings and ideals

16D70 Structure and classification (except as in <a href="#code:16Gxx">16Gxx</a>), direct sum decomposition, cancellation

16D80 Other classes of modules and ideals [See also <a href="#code:16G50">16G50</a>]

16D90 Module categories [See also <a href="#code:16Gxx">16Gxx</a>, <a href="#code:16S90">16S90</a>]; module theory in a category-theoretic context; Morita equivalence and duality