• Title, Summary, Keyword: bi-derivation

### ON GENERALIZED SYMMETRIC BI-DERIVATIONS IN PRIME RINGS

• Ozturk, M. Ali;Sapanci, Mehmet
• East Asian mathematical journal
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• v.15 no.2
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• pp.165-176
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• 1999
• After the derivation was defined in  by Posner a lot of researchers studied the derivations in ring theory in different manners such as in , , , ..., etc. Furthermore, many researches followed the definition of the generalized derivation(, , , ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.

### ON SYMMETRIC BI-GENERALIZED DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

• Kim, Kyung Ho
• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.179-189
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• 2019
• In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

### ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS

• Jung, Yong-Soo;Park, Kyoo-Hong
• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.959-967
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• 2011
• Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

### SYMMETRIC BI-(f, g)-DERIVATIONS IN LATTICES

• Kim, Kyung Ho;Lee, Yong Hoon
• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.491-502
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• 2016
• In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.

### SOME PROPERTIES OF SYMMETRIC BI-(σ, Τ)-DERIVATIONS IN NEAR-RINGS

• Ceven, Yilmaz;Ozturk, Mehmet Ali
• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.487-491
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• 2007
• In this paper, we introduce a symmetric $bi-({\sigma},\;{\tau})-derivation$ in a near-ring and generalize some of the results in [5, 6, 8, 9].

### ON SYMMETRIC BI-f-DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

• Kim, Kyung Ho
• East Asian mathematical journal
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• v.36 no.1
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• pp.1-11
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• 2020
• In this paper, we introduce the notion of symmetric bi-f-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if D is a symmetric bi-f-derivation of L, then D(x → y, z) = f(x) → D(y, z) for all x, y, z ∈ L.

### ON SYMMETRIC BI-f-DERIVATIONS OF SUBTRACTION ALGEBRAS

• Kim, Kyung Ho
• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.441-451
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• 2019
• In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.

### ON SYMMETRIC BI-DERIVATIONS OF B-ALGEBRAS

• Kayis, Sibel Altunbicak;Ozbal, Sule Ayar
• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.209-216
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• 2016
• In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.

### SYMMETRIC BI-f-MULTIPLIERS OF INCLINE ALGEBRAS

• Kim, Kyung Ho;Lee, Yong Hoon
• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.443-451
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• 2016
• In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

### SYMMETRIC BI-DERIVATIONS OF BCH-ALGEBRAS

• Kim, Kyung Ho
• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.561-573
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• 2015
• The aim of this paper is to introduce the notion of left-right (resp. right-left) symmetric bi-derivation of BCH-algebras and some related properties are investigated.