اصل موضعی سراسری برای مدولهای همولو‍‍ژی موضعی تعمیم یافته

نویسنده
دانشگاه اراک
چکیده
ایده الی از آن باشد. هدف از این مقاله، بیان و اثبات اصل I حلقه ای نوتری و جابجایی و R فرضکنید

، کوچکترین عدد صحیحی استکه aI (M;N) می باشد که aI (M;N) موضعی-سراسری برای بعد آرتینی

-مدول متناهی R ، آرتینی نیست. نشان می دهیم، برای HI

i (M;N) مدول های همولوژی موضعی تعمیم یافته

متناهی CoassR(HI

aI (M;N)(M;N)) ، هرگاه مجموعه N -مدول فشرده خطینیمه گسسته R وM مولد

باشد، آنگاه

aI (M;N) = inffaIRp (Mp;p N)jp 2 Spec(R)g:
کلیدواژه‌ها

عنوان مقاله English

The local-global principle for generalized local homology modules

نویسنده English

Marziyeh Hatamkhani
Arak University
چکیده English

Let R be a commutative noetherian ring and I be an ideal of R. The aim of this paper is to establish the local-global principle for the generalized local homology modules a_I(M,N), where a_I(M,N) is the smallest integer such that the generalized local homology module of M,N is not artinian. For a finitely generated R- module M and a linearly compact R-module N with the set CoassR(HI_aI (M;N)(M;N)) finite, we show that aI (M;N) = inffaIRp (Mp;p N)jp 2 Spec(R)g:

کلیدواژه‌ها English

artinianness dimension
generalized local homology modules
linearly compact modules
[1] M.P. Brodmann and R.Y. Sharp, Local cohomology; An algebraic introduction
with geometric applications, Cambridge: Cambridge University Press.
[2] N.T. Cuong and T.T. Nam , On the co-localization, co-support and coassociated
primes of local homology modules, Vietnam J. Math, 29, (2001),
no. 4, 359–368.
9
[3] N.T. Cuong and T.T. Nam, A local homology theory for linearly compact
modules, J. Algebra, 319, (2008), no. 11, 4712–4737.
[4] C.U. Jensen, Les Foncteurs Dérivés de l im􀀀 et leurs Applications en Théorie
des Modules, Springer-Verlag, Berlin/Heidelberg/New York, 1972.
[5] G. Faltings, Der endlichkeitssatz in der lokalen kohomologie, Math. Ann. ,
255, (1981), 45–56.
[6] M. Hatamkhani, Serre subcategory, generalized local homology and generalized
local cohomology modules, IEJA., 38, (2025), 228–242.
[7] M. Hatamkhani and K. Divaani-Aazar, On the vanishing of local homology
modules, Glasgow Math., 55, (2013), 457–464.
[8] I.G. MacDonald, Duality over complete local rings, Topology, 1, (1962),
213–235.
[9] I.G. MacDonald, Secondary representation of modules over a commutative
ring, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa,
INDAM, Rome, 1971), pp. 23–43. Academic Press, London, 1973.
[10] E. Matlis, The Koszul complex and duality, Comm. Algebra, 1, (1974), no.
2, 87–144.
[11] L. Melkersson and P. Schenzel, The co-localization of an Artinian module,
Proc. Edinburgh Math. Soc, (2) 38, (1995), no. 1, 121–131.
[12] T. T. Nam, A finiteness result for co-associated and associated primes of
generalized local homology and cohomology modules, Comm. Algebra 37,
(2009), no. 5, 1748–1757.
[13] T. T. Nam, Co-support and coartinian modules, Algebra Colloq, 15, (2008),
no. 1, 83–96.
[14] T. T. Nam, Left-derived functors of the generalized I-adic completion and
generalized local homology, Comm. Algebra, 38, (2010), no. 2, 440–453.
[15] A. Ooishi, Matlis duality and width of a module, Hiroshima Math. J., 6
(1976), 573-587.
[16] J. Shen, X. Yang, The local-global principle for the artinianness dimensions,
Comm. Algebra, 52, (2024), no. 12, 5396–5404.
[17] S. Yassemi, Coassociated primes, Comm. Algebra, 23, (1995), 1473–1498.
[18] D. N. Yen and T. T. Nam, Generalized local homology and duality, Internat.
J. Algebra Comput, 29, (2019), no. 3, 581–601.
[19] D. N. Yen and T. T. Nam, Uber koassoziierte primideale, Math. Scand.,
63, (1988), no. 2, 196–211.
10