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    一類代數(shù)上的弱可加交換映射

    2019-10-28 02:19霍東華
    關(guān)鍵詞:代數(shù)

    霍東華

    摘要:設(shè)A是一個有單位元1的代數(shù).稱映射f:A→A是一個弱可加映射,如果滿足對任意的x,y∈A,存在tx,y,sx,y∈IF使得f(x+y)=tx,yf(x)+sx,yf (y)成立.本文證明了在一定的假設(shè)下,如果,是交換映射,則存在Ao(x)∈4和一個從4到Z(A)的映射Ai,使得對所有的x∈A有f(x)=λ0(x)x+ λ1(x).作為應(yīng)用,刻畫了Mn (IF)上一類交換的弱可加映射.

    關(guān)鍵詞:代數(shù); 交換映射; 弱可加映射

    中圖分類號:0152.2

    文獻標(biāo)志碼:A

    DOI: 10.3969/j.issn.1000-5641.2019.04.001

    [參考文獻]

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    [3]BRESAR M. Centralizing mappings and derivations in prirue rings [J]. Journal of Algebra, 1993, 156(2) : 385-394.

    [4] MAYNE J H. Centralizing automorphisms of prime rings [J]. Canadian Matheruatical Bulletin, 1976, 19(1):113-115.

    [5]BRESAR M, MARTINDLE W S, MIERS C R. Centralizing maps in prime ring with involution [Jl Journal ofAlgebra, 1993, 161(2): 342-357.

    [6]LEE T K.σ-Commuting mappings in semiprime rings [J]. Communications in Algebra, 2001, 29(7): 2945-2951.

    [7]LEE T K. Derivations and centralizing mappings in prime rings [J]. Taiwanese Journal of Mathematics, 1997,1(3): 333-342.

    [8]LEE T C. Derivations and centralizing maps on skew elements [J] . Soochow Journal of Mathematics, 1998, 24(4):273-290.

    [9]FILIPPIS V D, DHARA B. Some results concerning n - σ-centralizing mappings in semiprime rings [J]. ArabianJournal of Mathematics, 2014, 3(1): 15-21.

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    [11]LI Y B, WEI F. Semi-centralizing maps of generalized matrix algebras [J]. Linear Algebra and its Applications,2012, 436(5): 1122-1153.

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