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研究生:陳東賢
研究生(外文):Tung-Shyan Chen
論文名稱:環上等式
論文名稱(外文):Identities in Rings with Additional Structures
指導教授:貝德貝德引用關係柯文峰
指導教授(外文):K.I. BeidarWen-Fong Ke
學位類別:博士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:43
外文關鍵詞:derivationgraded polynomial identitysuperalgebragraded-algebrasuperderivation
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In this thesis we consider some identities in rings having some additional structures.
There are three subjects:

(1) Special identities with (a,b)-derivations.
Let R be a prime ring. In 1993 Breˇsar studied the identity f1(x) f2(y) =f3(x) f4(y) for all x,y 2 R where each fi is a derivation of R. In 1997 Chang considered a more general case when f2 and f3 are (a,b)-derivations, f1 is an (a,a)-derivation and f4 is a (b,b)-derivation. We consider a more general case when each fi is an (ai,bi)-derivation. We show that there exists an
invertible element t in symmetric Martindale ring of quotients of R such that
f1(x) = f3(x)t and f4(x) = t f2(x) for all x 2 R.

(2) On graded polynomial identities with an antiautomorphism.
Let G be a commutative monoid with cancellation and let R be a strongly
G-graded associative algebra with finite G-grading and with an antiautomorphism.
Suppose that R satisfies a graded polynomial identity with an antiautomorphism.
We show that R is a PI algebra.

(3) Posner’s theorems for superderivations on superalgebras.
Let A = A0 A1 be a graded-prime associative superalgebra over a commutative
associative ring F with 1
2 , and let Zs(A) be its supercenter. If d is a
superderivation of A such that [x,d(x)]s 2 Zs(A) for all x 2 A, then either A
is commutative, or d(A0) = 0 and d(A1) Z(A), in particular, d(A) = 0 if
|d| = 0. On superalgebras, the composition of two nonzero superderivations
may still be a superderivation.
1 Introduction 2
1.1 (a,b)-derivations . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Graded Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Superalgebras . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Special Identities with (a,b)-derivations 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Proofs of Main Theorems . . . . . . . . . . . . . . . . . . . . . 16
3 On Graded Polynomial Identities with An Antiautomorphism 22
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Proof of Main Theorem . . . . . . . . . . . . . . . . . . . . . . 25
4 Posner’s Theorems for Superderivations on Superalgebras 34
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Proofs of the Main Results . . . . . . . . . . . . . . . . . . . . 35
4.3 The Composition of Two Superderivations . . . . . . . . . . . 41
[1] S.A. Amitsur, Rings with involution, Israel J. Math. 6 (1968), 99–106.
[2] S.A. Amitsur, Identities in rings with involution, Israel J. Math. 7 (1969), 63–68.
[3] Yu.A. Bahturin and M.V. Zaicev, Identities of graded algebras, J. Algebra 205
(1998), 1–12.
[4] K.I. Beidar, On functional identities and commuting additive mappings, Comm.
Algebra 26 (1998), 1819–1850.
[5] K.I. Beidar and M.A. Chebotar, On functional identities and d-free subsets of rings,
I, Comm. Algebra 28 (2000), 3925–2951.
[6] K.I. Beidar and M.A. Chebotar, When a graded PI algebra is a PI algebra?, to
appear in Comm. Algebra.
[7] K.I. Beidar, Y Fong, P.-H Lee and T.-L Wong, On additive maps of prime rings
satisfying Engel condition, Comm. Algebra 25 (1997), 3889–3902.
[8] K.I. Beidar, Y Fong, W.-F. Ke and C.-H. Lee, Posner’s Theorem for generalized
(s,d)-derivations, Lie Algebra, Rings and Related Topics, Springer-Verlag (2000),
5–12.
[9] K.I. Beidar, Y Fong and X.K. Wong, Posner and Herstein theorems for derivations
of 3-prime near-rings, Comm. Algebra 24 (1996),1581–1589.
[10] K.I. Beidar and W.S. Martindale 3rd, On functional identities in prime rings with
involution, J. Algebra 203 (1998), 491–532.
[11] K.I. Beidar, W.S. Martindale 3rd and A.V. Mikhalev, Rings with generalized identities,
Marcel Dekker, Inc., 1996.
[12] H. E. Bell and W. S. Martindale 3rd, Centralizing mappings of semiprime rings,
Canad. Math. Bull. 30 (1987), 92–101.
[13] J. Bergen and M. Cohen, Actions of commutative Hopf algebras, Bull. London
Math. Soc. 18 (1986), 159–164.
[14] M. Breˇsar, Centralizing mappings and derivations in prime rings, J. Algebra 156
(1993), 385–394.
[15] M. Breˇsar, On generalized biderivations and related maps, J. Algebra 172 (1995),
764–786.
[16] J.-C. Chang, A special identity of (a,b)-derivations and its consequences, Taiwanese
J. Math. 1 (1997), 21–30.
[17] J.-C. Chang, A note on (a,b)-derivations, Chinese J. Math. 19 (1991), 277–285.
[18] J.-C. Chang and J.-S. Lin, (a,b)-derivation with nilpotent values Chinese J. Math.
22 (1994), 349–355.
[19] M.A. Chebotar, A note on certain subrings and ideals of prime rings, Comm. Algebra
26 (1998), 107–116.
[20] T.-S. Chen, Special identities with (a,b)-derivations, Riv. Mat. Univ. Parma 5
(1996), 109–119.
[21] I.N. Herstein, A note on derivation II, Canad. Math. Bull. 22 (1979), 509–511.
[22] I.N. Herstein, Special simple rings with involution, J. Algebra 6 (1967), 369–375.
[23] I.N. Herstein, Rings with involution, Chicago Lectures in Mathematics, 1976.
[24] I.N. Herstein, On the Lie structure of an associative ring, J. Algebra 14 (1970),
561–571.
[25] M. Hongan, A generalization of a theorem of Posner, Math. J. Okayama Univ. 33
(1991), 97–101.
[26] S.K. Jain, Prime rings having one-sided ideal with polynomial identity coincide with
special Johnson rings, J. Algebra 19 (1971), 125–130.
[27] A.V. Kelarev, On semigroup graded PI algebras, Semigroup Forum 47 (1993), 294–
298.
[28] M. Ke¸pczyk and E. Puczyłowski, Rings which are sums of two subrings satisfying
polynomial identities, Comm. Algebra 29 (2001), 2059–2065.
[29] V. K. Kharchenko and A. Z. Popov, Skew derivations of prime rings, Comm. Algebra
20 (1992), 3321–3345.
[30] T.-K. Lee, s-commuting mapping in semiprime rings, Comm. Algebra 29
(2001),2945–2951.
[31] W.S. Martindale 3rd, Prime rings satisfying a generalized polynomial identity, J.
Algebra 12 (1969), 576–584.
[32] W.S. Martindale 3rd, Rings with involution and polynomial identities, J. Algebra 11
(1969), 186–194.
[33] J. C. McConnell and J. C. Robson, Noncommutative noetherian rings, John Wiley
& Sons, 1987.
[34] S. Montgomery, Hopf algebras and their actions on rings, Regional Conference
Series in Math., 82. Amer. Math. Soc., Providence, Rhode Island, 1993.
[35] S. Montgomery, Constructing simple Lie superalgebras from associative graded
algebras, J. Algebra 195 (1997), 558–579.
[36] F. Montaner, On the Lie structure of associative superalgebras, Comm. Algebra
26(7) (1998), 2337–2349.
[37] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093–
1100.
[38] L.H. Rowen, Polynomial identities in ring theory, Academic Press, Inc., 1980.
[39] S.K. Sehgal and M.V. Zaicev, Graded identities of group algebras Comm. Algebra
30 (2002), 489–505.
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