signature=5dd921e127ca4260f7a83c6b9e1f8542,F -signature exists | SpringerLink

1.

Aberbach, I.M.: The existence of the F-signature for rings with large ℚ-Gorenstein locus. J. Algebra 319(7), 2994–3005 (2008). MR2397419 (2009c:13009)

2.

Aberbach, I.M., Enescu, F.: The structure of F-pure rings. Math. Z. 250(4), 791–806 (2005). MR2180375

3.

Aberbach, I.M., Enescu, F.: When does the F-signature exist? Ann. Fac. Sci. Toulouse Math. (6) 15(2), 195–201 (2006). MR2244213 (2007d:13004a)

4.

Aberbach, I.M., Leuschke, G.J.: The F-signature and strong F-regularity. Math. Res. Lett. 10(1), 51–56 (2003). MR1960123 (2004b:13003)

5.

Aberbach, I.M., MacCrimmon, B.: Some results on test elements. Proc. Edinb. Math. Soc. (2) 42(3), 541–549 (1999). MR1721770 (2000i:13005)

6.

Blickle, M., Enescu, F.: On rings with small Hilbert-Kunz multiplicity. Proc. Am. Math. Soc. 132(9), 2505–2509 (2004) (electronic). MR2054773 (2005b:13029)

7.

Blickle, M., Schwede, K., Tucker, K.: F-signature of pairs and the asymptotic behavior of Frobenius splittings. arXiv:1107.1082

8.

Bourbaki, N.: Commutative Algebra. Chapters 1–7. Elements of Mathematics. Springer, Berlin (1998). Translated from the French, Reprint of the 1989 English translation. MR1727221 (2001g:13001)

9.

Brion, M., Kumar, S.: Frobenius Splitting Methods in Geometry and Representation Theory. Progress in Mathematics, vol. 231. Birkhäuser, Boston (2005). MR2107324 (2005k:14104)

10.

Dutta, S.P.: Frobenius and multiplicities. J. Algebra 85(2), 424–448 (1983). 725094 (85f:13022)

11.

Enescu, F., Yao, Y.: The lower semicontinuity of the Frobenius splitting numbers. Math. Proc. Camb. Philos. Soc. (2010). doi:10.1017/S0305004110000484

12.

Hara, N., Yoshida, K.-I.: A generalization of tight closure and multiplier ideals. Trans. Am. Math. Soc. 355(8), 3143–3174 (2003) (electronic). MR1974679 (2004i:13003)

13.

Hochster, M.: Foundations of Tight Closure Theory. Lecture Notes from a Course Taught on the University of Michigan, Fall 2007 (2007)

14.

Hochster, M., Huneke, C.: Tight closure and strong F-regularity. Mém. Soc. Math. Fr. (N.S.) 38, 119–133 (1989). Colloque en l’honneur de Pierre Samuel (Orsay, 1987). MR1044348 (91i:13025)

15.

Hochster, M., Huneke, C.: Tight closure, invariant theory, and the Briançon-Skoda theorem. J. Am. Math. Soc. 3(1), 31–116 (1990). MR1017784 (91g:13010)

16.

Hochster, M., Roberts, J.L.: Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay. Adv. Math. 13, 115–175 (1974). MR0347810 (50 #311)

17.

Hochster, M., Roberts, J.L.: The purity of the Frobenius and local cohomology. Adv. Math. 21(2), 117–172 (1976). MR0417172 (54 #5230)

18.

Huneke, C.: Tight Closure and Its Applications. CBMS Regional Conference Series in Mathematics, vol. 88 (1996). Published for the Conference Board of the Mathematical Sciences, Washington, DC. With an appendix by Melvin Hochster. MR1377268 (96m:13001)

19.

Huneke, C., Leuschke, G.J.: Two theorems about maximal Cohen-Macaulay modules. Math. Ann. 324(2), 391–404 (2002). MR1933863 (2003j:13011)

20.

Kunz, E.: Characterizations of regular local rings for characteristic p. Am. J. Math. 91, 772–784 (1969). MR0252389 (40 #5609)

21.

Kunz, E.: On Noetherian rings of characteristic p. Am. J. Math. 98(4), 999–1013 (1976). MR0432625 (55 #5612)

22.

Lyubeznik, G., Smith, K.E.: Strong and weak F-regularity are equivalent for graded rings. Am. J. Math. 121(6), 1279–1290 (1999). MR1719806 (2000m:13006)

23.

Lyubeznik, G., Smith, K.E.: On the commutation of the test ideal with localization and completion. Trans. Am. Math. Soc. 353(8), 3149–3180 (2001) (electronic). MR1828602 (2002f:13010)

24.

Matsumura, H.: Commutative Algebra, 2nd edn. Mathematics Lecture Note Series, vol. 56. Benjamin/Cummings, Reading (1980). MR575344 (82i:13003)

25.

Monsky, P.: The Hilbert-Kunz function. Math. Ann. 263(1), 43–49 (1983). MR697329 (84k:13012)

26.

Monsky, P.: Rationality of Hilbert-Kunz multiplicities: a likely counterexample. Mich. Math. J. 57, 605–613 (2008). Special volume in honor of Melvin Hochster. 2492471 (2010g:13026)

27.

Schwede, K.: Centers of F-purity. Math. Z. (2009). doi:10.1007/s00209-009-0536-5

28.

Shepherd-Barron, N.I.: On a problem of Ernst Kunz concerning certain characteristic functions of local rings. Arch. Math. (Basel) 31(6), 562–564 (1978/79). 531569 (81e:13012)

29.

Singh, A.K.: The F-signature of an affine semigroup ring. J. Pure Appl. Algebra 196(2–3), 313–321 (2005). MR2110527 (2005m:13010)

30.

Smith, K.E., Van den Bergh, M.: Simplicity of rings of differential operators in prime characteristic. Proc. Lond. Math. Soc. (3) 75(1), 32–62 (1997). MR1444312 (98d:16039)

31.

Swan, R.G.: Algebraic K-Theory. Lecture Notes in Mathematics, vol. 76. Springer, Berlin (1968). 0245634 (39 #6940)

32.

Vraciu, A.: Local cohomology of Frobenius images over graded affine algebras. J. Algebra 228(1), 347–356 (2000). 1760968 (2001b:13023)

33.

Watanabe, K.-i., Yoshida, K.-i.: Hilbert-Kunz multiplicity and an inequality between multiplicity and colength. J. Algebra 230(1), 295–317 (2000). MR1774769 (2001h:13032)

34.

Watanabe, K.-i., Yoshida, K.-i.: Minimal relative Hilbert-Kunz multiplicity. Ill. J. Math. 48(1), 273–294 (2004). 2048225 (2005b:13033)

35.

Watanabe, K.-i., Yoshida, K.-i.: Hilbert-Kunz multiplicity of three-dimensional local rings. Nagoya Math. J. 177, 47–75 (2005). 2124547 (2005m:13026)

36.

Yao, Y.: Modules with finite F-representation type. J. Lond. Math. Soc. (2) 72(1), 53–72 (2005). 2145728 (2006b:13012)

37.

Yao, Y.: Observations on the F-signature of local rings of characteristic p. J. Algebra 299(1), 198–218 (2006). MR2225772 (2007k:13007)

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