共查询到20条相似文献,搜索用时 31 毫秒
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Let R be an associative ring with unit and denote by the homotopy category of complexes of projective left R-modules. Neeman proved the theorem that is -compactly generated, with the category of left bounded complexes of finitely generated projective R-modules providing an essentially small class of such generators. Another proof of Neeman's theorem is explained, using recent ideas of Christensen and Holm, and Emmanouil. The strategy of the proof is to show that every complex in vanishes in the Bousfield localization . 相似文献
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Jan O. Kleppe 《Journal of Pure and Applied Algebra》2018,222(3):610-635
Let be the scheme parameterizing graded quotients of with Hilbert function H (it is a subscheme of the Hilbert scheme of if we restrict to quotients of positive dimension, see definition below). A graded quotient of codimension c is called standard determinantal if the ideal I can be generated by the minors of a homogeneous matrix . Given integers and , we denote by the stratum of determinantal rings where are homogeneous of degrees .In this paper we extend previous results on the dimension and codimension of in to artinian determinantal rings, and we show that is generically smooth along under some assumptions. For zero and one dimensional determinantal schemes we generalize earlier results on these questions. As a consequence we get that the general element of a component W of the Hilbert scheme of is glicci provided W contains a standard determinantal scheme satisfying some conditions. We also show how certain ghost terms disappear under deformation while other ghost terms remain and are present in the minimal resolution of a general element of . 相似文献
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Gangyong Lee Jae Keol Park S. Tariq Rizvi Cosmin S. Roman 《Journal of Pure and Applied Algebra》2018,222(9):2427-2455
Let V be a module with . V is called a quasi-Baer module if for each ideal J of S, for some . On the other hand, V is called a Rickart module if for each , for some . For a module N, the quasi-Baer module hull (resp., the Rickart module hull ) of N, if it exists, is the smallest quasi-Baer (resp., Rickart) overmodule, in a fixed injective hull of N. In this paper, we initiate the study of quasi-Baer and Rickart module hulls. When a ring R is semiprime and ideal intrinsic over its center, it is shown that every finitely generated projective R-module has a quasi-Baer hull. Let R be a Dedekind domain with F its field of fractions and let be any set of R-submodules of . For an R-module with , we show that has a quasi-Baer module hull if and only if is semisimple. This quasi-Baer hull is explicitly described. An example such that has no Rickart module hull is constructed. If N is a module over a Dedekind domain for which is projective and , where is the torsion submodule of N, we show that the quasi-Baer hull of N exists if and only if is semisimple. We prove that the Rickart module hull also exists for such modules N. Furthermore, we provide explicit constructions of and and show that in this situation these two hulls coincide. Among applications, it is shown that if N is a finitely generated module over a Dedekind domain, then N is quasi-Baer if and only if N is Rickart if and only if N is Baer if and only if N is semisimple or torsion-free. For a direct sum of finitely generated modules, where R is a Dedekind domain, we show that N is quasi-Baer if and only if N is Rickart if and only if N is semisimple or torsion-free. Examples exhibiting differences between the notions of a Baer hull, a quasi-Baer hull, and a Rickart hull of a module are presented. Various explicit examples illustrating our results are constructed. 相似文献
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Pooyan Moradifar Shahab Rajabi Siamak Yassemi 《Journal of Pure and Applied Algebra》2018,222(11):3757-3773
Given a non-unit, non-zero-divisor, central element x of a ring Λ, it is well known that many properties or invariants of Λ determine, and are determined by, those of and . In the present paper, we investigate how the property of “being tilting” behaves in this situation. It turns out that any tilting module over Λ gives rise to tilting modules over and after localization and passing to quotient respectively. On the other hand, it is proved that under some mild conditions, a module over Λ is tilting if its corresponding localization and quotient are tilting over and respectively. 相似文献
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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《Finite Fields and Their Applications》2006,12(1):103-127
For any sequence over , there is an unique 2-adic expansion , where and are sequences over and can be regarded as sequences over the binary field naturally. We call and the level sequences of . Let be a primitive polynomial of degree over , and be a primitive sequence generated by . In this paper, we discuss how many bits of can determine uniquely the original primitive sequence . This issue is equivalent with one to estimate the whole nonlinear complexity, , of all level sequences of . We prove that is a tight upper bound of if is a primitive trinomial over . Moreover, the experimental result shows that varies around if is a primitive polynomial over . From this result, we can deduce that is much smaller than , where is the linear complexity of level sequences of . 相似文献
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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