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The Structure of Schur Algebras Sk(n, p) for n ≥ p
Changchang XI
Journal:

Canadian Journal of Mathematics / Volume 44 / Issue 3 / 01 June 1992

Published online by Cambridge University Press:

20 November 2018, pp. 665-672

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01 June 1992
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By exploiting the known quasi-heredity of Schur algebras, the structure of basic algebras of the Schur algebras Sk(n, p) for n ≥ p over an algebraically closed field k is completely determined.

Extensions that are Submodules of their Quotients
F. Okoh, F. Zorzitto
Journal:

Canadian Mathematical Bulletin / Volume 33 / Issue 1 / 01 March 1990

Published online by Cambridge University Press:

20 November 2018, pp. 93-99

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01 March 1990
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Let 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.

The Duals of the Camillo-Zelmanowitz Formulas for Goldie Dimension
Joel K. Haack
Journal:

Canadian Mathematical Bulletin / Volume 25 / Issue 3 / 01 September 1982

Published online by Cambridge University Press:

20 November 2018, pp. 325-334

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01 September 1982
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The duals of the Camillo-Zelmanowitz formulas for Goldie dimension are shown to hold for Varadarajan's notion of corank, subject to the existence of certain cocomplements. In particular, the formulas hold for modules over perfect rings. Also, if R is semiperfect, then the vector space dimension formulas hold for all modules over R for Goldie dimension iff they hold for corank iff R is semisimple.