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https://doi.org/10.3336/gm.47.1.08

On (anti-)multiplicative generalized derivations

Daniel Eremita ; Department of Mathematics and Computer Science, FNM, University of Maribor, 2000 Maribor, Slovenia
Dijana Ilisevic   ORCID icon orcid.org/0000-0002-0833-3016 ; Department of Mathematics, University of Zagreb, Bijenička 30, P.O.Box 335, 10002 Zagreb, Croatia

Puni tekst: engleski, pdf (138 KB) str. 105-118 preuzimanja: 247* citiraj
APA 6th Edition
Eremita, D. i Ilisevic, D. (2012). On (anti-)multiplicative generalized derivations. Glasnik matematički, 47 (1), 105-118. https://doi.org/10.3336/gm.47.1.08
MLA 8th Edition
Eremita, Daniel i Dijana Ilisevic. "On (anti-)multiplicative generalized derivations." Glasnik matematički, vol. 47, br. 1, 2012, str. 105-118. https://doi.org/10.3336/gm.47.1.08. Citirano 26.10.2021.
Chicago 17th Edition
Eremita, Daniel i Dijana Ilisevic. "On (anti-)multiplicative generalized derivations." Glasnik matematički 47, br. 1 (2012): 105-118. https://doi.org/10.3336/gm.47.1.08
Harvard
Eremita, D., i Ilisevic, D. (2012). 'On (anti-)multiplicative generalized derivations', Glasnik matematički, 47(1), str. 105-118. https://doi.org/10.3336/gm.47.1.08
Vancouver
Eremita D, Ilisevic D. On (anti-)multiplicative generalized derivations. Glasnik matematički [Internet]. 2012 [pristupljeno 26.10.2021.];47(1):105-118. https://doi.org/10.3336/gm.47.1.08
IEEE
D. Eremita i D. Ilisevic, "On (anti-)multiplicative generalized derivations", Glasnik matematički, vol.47, br. 1, str. 105-118, 2012. [Online]. https://doi.org/10.3336/gm.47.1.08

Sažetak
Let R be a semiprime ring and let F, f : R → R be (not necessarily additive) maps satisfying F(xy)=F(x)y+xf(y) for all x,y R. Suppose that there are integers m and n such that F(uv)=mF(u)F(v)+nF(v)F(u) for all u, v in some nonzero ideal I of R. Under some mild assumptions on R, we prove that there exists c C(I⊥⊥) such that c=(m+n)c2, nc[I⊥⊥, I⊥⊥]=0 and F(x)=cx for all x I⊥⊥. The main result is then applied to the case when F is multiplicative or anti-multiplicative on I.

Ključne riječi
Additivity; ring; semiprime ring; prime ring; derivation; generalized derivation; homomorphism; anti-homomorphism

Hrčak ID: 82574

URI
https://hrcak.srce.hr/82574

Posjeta: 465 *