Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras
Keyword(s):
Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.
1984 ◽
Vol 27
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pp. 247-250
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1978 ◽
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pp. 817-829
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pp. 959-976
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pp. 387-403
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pp. 31-38
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pp. 1950035
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pp. 265-273
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pp. 1795-1812
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pp. 1850202
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