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991.
Using the concept of prime submodule for M ∈ R-Mod, P ∈ Spec(M), and N ∈ σ[M], we define when N is P-Mtame \ (Mtame) module. This concept generalizes the concept\ of P-tame (tame) modules. For M ∈ R-Mod and τ ∈M-tors, we use the concept of τ M -Gabriel dimension and we study the relationship between Mtame modules and τ M -Gabriel dimension. We find equivalent conditions for a module M progenerator in σ[M] with τ M -Gabriel dimension to have τ M -Gabriel correspondence in terms of the P-Mtame modules. This result extends the results by Albu et al. and Kim and Krause. 相似文献
992.
In this article, we study the hereditary torsion theory defined by the set of associated primes of principle ideals of an integral domain, which is called the g-torsion theory. We first discuss some general properties of g-torsion theories, and after that give some applications of them. For example, we generalize a characterization of reflexive modules over quasi-normal domains to a class of non-Noetherian domains. Among other things, a characterization of coherent domains of weak Gorenstein global dimension at most two is also given in terms of Gorenstein projectivity (or Gorenstein flatness) of injective modules relative to the g-torsion theory. 相似文献
993.
994.
The Hodge spectrum is an important analytic invariant of singularities encoding the Hodge filtration and the monodromy of the Milnor fiber. However, explicit formulas exist in only a few cases. In this article, the main result is a combinatorial formula for the Hodge spectrum of any homogeneous polynomials in three variables whose zero locus is a projective curve arrangement having only ordinary multiple points. 相似文献
996.
997.
Sang Bum Lee 《代数通讯》2013,41(3):1232-1240
Strongly flat modules were introduced by Bazzoni–Salce [3] and used to characterize almost perfect domains. Here we wish to study strongly flat modules, more generally, over Matlis domains; these are integral domains R such that the field of quotients Q has projective dimension 1. In Section 2, criteria are proved for strong flatness. We also prove that over arbitrary domains, strongly flat submodules of projective modules are projective (Theorem 3.2), in particular, strongly flat ideals are projective (Corollary 3.4) and use these results to show that the strongly flat dimension (which makes sense over Matlis domains) coincides with the projective dimension whenever it is > 1. 相似文献
998.
999.
The free nonassociative algebra has two subspaces which are closed under both the commutator and the associator: the Akivis elements and the primitive elements. Every Akivis element is primitive, but there are primitive elements which are not Akivis. Using a theorem of Shestakov, we give a recursive formula for the dimension of the Akivis elements. Using a theorem of Shestakov and Umirbaev, we prove a closed formula for the dimension of the primitive elements. These results generalize the Witt dimension formula for the Lie elements in the free associative algebra. 相似文献
1000.