章聚樂

1963年畢業於安徽師範大學數學系。安徽師範大學代數教授、德國《數學文摘》雜誌社評論員、安徽師範大學數系研究室主任、基礎數學研究生導師、享受國務院特殊津貼。

基本信息

人物履歷

安徽師範大學數學計算機科學學院教授,基礎數學研究生導師,1937年9月生,安徽省樅陽縣人,1963年7月畢業於皖南大學(今安徽師範大學)數學系。曾任安徽師範大學數學系代數教研室副主任,代數研究室主任,數學系副主任,德國《數學文摘》雜誌社評論員,安徽師範大學教學督導員,《安徽師大學報》編委。享受政府特殊津貼,獲安徽省1993年科技進步獎,獲曾憲梓教育基金會1997年高等師範院校教師獎。

自工作以來,一直從事與代數

學相關課程的教學和《環論與同調代數》的研究工作。1979年開始參與培養基礎數學研究生,1986年開始單獨培養基礎數學研究生。先後講授大學本科生的基礎課和選修課有《高等代數》,《近世代數》,《數論》,《群論》,《環與域》和《代數學》,研究生的基礎課和專業課有《基礎代數》,《除環上線性代數》,《環論》,《李代數》,《交換代數》,《多重線性代數》,《模論》,《同調代數》,《非奇異環與模》和《Von Neumann 正則環論》等十多門課程。教學認真負責,注意為人師表,教書育人,治學嚴謹,深受學生一致歡迎與尊敬,深得領導與同事們的高度評價與稱讚,1982年獲安徽師範大學教學質量優秀獎,

為國家培養了十多名代數學研究生和一批數學專業的優秀人才。

成就及榮譽

多年來,在《同調代數》,《Von Neumann 正則環論》和《矩陣的廣義逆》等理論方面有系統深入研究,其中《 Von Neumann 正則環及其推廣》的研究被公認為居國內領先地位。先後在《Comm. in Algebra》(U.S.A.)、《Comm. Math.》(Poland)、《Internat. J. Math. and Math.Sci.》(U.S.A.)、《Algebra Collequium》、《Kobe J. Math.》(Japan)、《Southeast Asian Bull. Math.》、《Acta Math. Vietnamica》、《科學通報》、《數學年刊》、《數學進展》、《數學研究與評論》、《東北數學》、《數學雜誌》、《數學季刊》等國內外重要雜誌上發表論文40餘篇,

主要有: 1. Von Neumann Regularity of SF-Rings (with Du Xianneng), Algebra,21(7)(1993),2445-2451, M

R94e:16021, Zbl.791(1994):16009.

2. 每個極大左理想是理想的完全冪等環,科學

通報,36(20)(1991),1529-1531, Zbl.762 (1993):16005. Fully Idempotent Rings Whose Every Maximal Left Ideal Is an Ideal,Chinese Science Bulletin,37(13)(1992),1065-1068.

3. Generalizations of Principal Injectivity (with Wu Jun),Algebra Colloquium, 6(3)(1999),277-282,

4. Von Neumann 正則環和SF-環(與杜先能合作),數學年刊,14A(1)(1993),6-10, MR94c:16012, Zbl.801(1995):16007. On Von Neumann Regular Rings and SF-Rings(with Du Xianneng),Chinese J.of Contemporary Mathematics,14(1)(1993),9-13, MR94j:16016.

5. Hereditary Rings Containing an Injective Maximal Left Ideal (with Du Xianneng),Algebra,21(12)(1993),4473-4479, MR94j:16017, Zbl.803(1995):16010.

6. 每個本質左理想是理想的MERT環(與胡衛群合作),數學年刊,15A(2)(1994),204-207, Zbl.808(1995):16015.

7. On a Question Concerning WCT Rings,Commentationes Mathematicae (Poland), 34 (1994),253-257, MR96c:16031, Zbl.827(1996):16002.

8. MELT右V-環是Von Neumann正則環(與杜先能合作),科學通報,39(17)(1994),1629,Zbl.839(1996):16010. MELT Right V-Rings Are Von Neumann Regular (with Du Xianneng),Chinese Science Bulletin,40(11)(1995),967-968.

9. Semiprime SF-Rings Whose Essential Left Ideals Are Two-Sided (with Du Xianneng) Internat.J.Math.& Math.Sci.(U.S.A.),17(3)(1994),617-618.

10. SF-Rings Whose Maximal Essential Left Ideals Are Ideals, Advances in Mathematics(數學進展),23(3)(1994),257-262.

11. Some Remarks on Von Neumann Regular Rings (with Du Xianneng),Kobe j. Math.(Japan),9(2)(1992),151-157, MR94a:16016, Zbl.780(1994):16008.

12. P-Injective Rings and Von Neumann Regular Rings, Northeastern Math.J.(東北數學),7(3)(1991),326-331, MR93e:16020, Zbl.765(1993):16005.

13. Left SF-Rings Whose Complement Left Ideals Are Ideals (with Du Xianneng),Acta Math.Vietnamica,17(1)(1992),157-159, MR93j:16008.

14. P-Injectivity and Artinian Semisimple Rings,J.of Math.Research and Exposition (數學研究與評論),11(4)(1991),578-585, MR92I:16008, Zbl.790 (1994):16008.

15. A Note Von Neumann Regular Rings, Southeast Asian Bulletin of Math.,22(2) (1998),231-235.

16. Characterizations of Strongly Regular Rings, Northeast. Math.J.(東北數學),10(3)(1994),359-364, MR96a:16007, Zbl.822(1995):16002.

17. P-內射環和半素環(與陳建龍合作),數學雜誌,11(1)(1991),29-34.

18. Endomorphism Rings of Generalized Quasi-Injective Modules,J.of Math. Research and Exposition(數學研究與評論),10(4)(1991),585-588, Zbl.793 (1992):1602

0.

19. 關於SF-環的幾點註記, 數學雜誌,14(2)(1994),197-202.

20. On fpp-Rings (with Du Xianneng),Chinese Quarterly J.of Math.(數學季刊),8(1)(1993),77-80.

21. P-內射環的某些研究 (與陳建龍合作),數學雜誌,12(2)(1992),141-145, Zbl.762 (1993):16002.

22. Strongly Regular Rings and SF-Rings(with Lu Rongdian),Northeast.Math.J.(東北數學),14(1)(1998),61-68.

23. 主左理想由若干個冪等元生成的環(與吳貴花合作),數學研究與評論,16(2)(1996),269-274, MR97c:16013.

24. Note on "Some New Results of P-Injective Rings" and "Regular Rings Are Very Regular" (with Xue Weimin), J.of Math.Research and Exposition (數學研究與評論),11(3)(1991),474-476, Zbl.780(1994):16007.

25. 關於McCoy定理(與杜先能合作),數學研究與評論,16(1)(1996),145-146, Zbl.849 (1996),16002.

26. Some Remarks on SF-Rings (with Du Xia

nneng),J.of Anhui Normal University (Natural Science),15(3)(1992),1-6.

27. 環上矩陣的Drazin逆(與杜先能合作),安徽師大學報 (自然科學版),19(4)(1996),305-308.

28. A Computational Method of Matrices,

J.of Anhui Normal University (Natural Science),1(2)(1974),45-60.

29. 結合環的可換性定理,安徽師大學報(自然科學版),7(2)(1984),14-18.

30. V-Rings Whose Essential Left Ideals Are Two-Sided (with Du Xianneng),J.Anhui Normal University (Natural Science),17(2)(1994),15-17, Zbl.864(1997):16006.

31. Von Neumann正則環( I ),安徽師大學報(自然科學版),13(3)(1990),13-18.

32. Von Neumann Regular Rings and P-V-Rings (with Wu Guihua),J.Anhui Normal University(Natural Science),17(4)(1994),1-5, Zbl.868(1997):16008.

33. 關於非奇異環, 安徽師大學報 (自然科學版),9(4)(1986),6-11.

34. Self Injective Rings and Regular Rings, Collected papers of 70th anniversary of the founding of Anhui Normal University,167-172, Anhui People's Press,1998.

35. P-內射環的幾個新結果(與陳建龍合

作),安徽師大學報(自然科學版),12 (2) (1989),6-11.

36. P-Injective Rings, Communications on Algebra (Anhui Math.Soc.),2(1988),31-40.

37. 半素子模的判別定理(與杜先能合作),安徽師大學報(自然科學版),12(4)(1989),9-13.

38. Right Semi-duo ∏-Regular Rings (with Wu Guihua),J.of Anhui Normal University (Natural Science),19(1)(1996),1-6.

39. 關於正則環的幾點註記(與吳貴花合作),安徽師大學報(自然科學版),19(3)(1996),203-206.

40. 具詣零單邊理想鏈條件的環,安徽師大學報(自然科學版),8(2)(1985) 6-10.

41. Ostrowski定理的推廣與套用(與張曉

東合作),安徽師大學報(自然科學版),20(2) (1997),115-118.

在上面的部分論文中,解決了在國外多種重要數學雜誌上所提出的有關《環論》與《同調代數》的18個公開問題 ,它們是:

(1)If R is a left hereditary ring containing an injective maximal left ideal, is R semi-simple Artinian ? (cf. Algebra,20(3)(1992),749-759)

(2) Is R sem-simple Artinian if a ring R contains an injective maximal left ideal and every maximal left ideal of R is projective ? (cf. Arch. Math.,28(1992),215-220)

(3) If every non-zero complement left ideal of a ring R contains a non-zero ideal and every non-zero ideal of R contains a non-zero complement left ideal, is R a left WCT ring ? (cf. Ann. Soc. Math. Poland,30(1991),491-500)

(4) Is R regular if R is a MELT ring and

every simple right R-module is flat ? (cf. Comm. in Algebra,20(3)(1992),749-759)

(5) Is R self-injective regular if R is an ELT right CE-injective ring whose simple right R-modules are flat ? (cf. Ricerche di Mathematica,33(2)(1984),147-157)

(6) Is R regular if R is an ELT fully right idempotent ring ? (cf. Comm. Korean Math. Soc.8(3)(1993),345-349)

(7) Is R regular if every left (and right) R-module is GP-injective ? (cf. Riv.Mat.Univ.Parma,22(5)(1996),183-188)

(8) Is a MELT right V-ring R von Neumann regular ? (cf. Ricerche di Mathematica,33(2)(1984),147-157) (9) Is a left V ring whose essential left ideals are two-sided regular ? (cf. Math.J.Okayama Univ.,20(1978),123-129)

(10) Is R von Neumann regular if R is a MELT fully idempotent ring ? (cf. Portugaliae Math.44(1)(1987),101-112)

(11) Is R von Neumann regular

if every left (and right) R-module is YJ-injective ? (cf. Riv.Mat.Univ.Parma,22(5)(1996),183-188)

(12) Is R strongly regular if every ideal of a ring R is idempotent and every maximal left ideal of R is an ideal ? (cf. Bull.Soc.Math.Belgium,41(1989),129-138)

(13) Is R regular if R is a MERT ring and R is fully left idempotent ? (cf. Ann.Univ.Ferrara,31(1985),49-61) (14) Is R strongly regular if every complement left ideal of a ring R is an ideal and every simple R-module is flat ? (cf. Acta Math. Vietnamica,13(2)(1988),71-79)

(15) If R is an ERT ring which is a one-sided V-ring, then is R a left and right V-ring ? (cf. Kyungpook Math.J.,32(2)(1992),219-228)

(16) Is R regular if R a semiprime ELT ring and every simple right R-module is flat ? (cf. Math.J.Okayama Univ.,22(1980),151-160)

(17) Is R regular if R is a MERT ring and every simple right R-module is flat ? (cf. Ann.Univ.Ferrara,31(1985),49-61)

(18) Is R of bounded index if R is an ERT regular ring ? (cf. Kyungpook Math.J.,32(2)(1992),219-228)

社會評價

在圓滿解決這些數學公開問題的一系列論文中,以及與這些這些數學公開問題有關的論文中,大部分研究成果具國際先進水平,得到了國內外同行專家的普遍關注與好評,多國學者和多位國內同行紛紛來信要求提供所發表的論文和相關資料。所發表論文中

很多都被美國《數學評論》、德國《數學文摘》全面摘評,同時被國內外同行專家廣泛引用。先後兩次領導《Von Neumann 正則環論及其推廣》等省教委下達的科研項目的研究,取得了一系列成果,1993年獲安徽省科技進步獎。事跡被收入《世界名人錄》、《當代中國科學家傳略》、《中國高等教育專家名典》、《

中國當代知名學者辭典》、《當代中國科學家與發明家大辭典》、《中國專家人才庫》、《安徽師大英才錄》和《世界數學家人名錄》等二十餘種大型辭典。

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