TY  - JOUR
T1  - Additivity of multiplicative generalized Jordan maps on triangular rings
AU  - Prakash, Om
AU  - Aziz, Sk
AU  - Ghosh, Arindam
PY  - 2025
DA  - January
Y2  - 2024
DO  - 10.24330/ieja.1488471
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 91
EP  - 111
VL  - 37
IS  - 37
LA  - en
AB  - This paper presents three different conditions for the additivity of a map on a triangular ring $\mathcal{T}$. First, we prove a map $\delta$ on $\mathcal{T}$ satisfying  $delta(a_1b_1+b_1a_1)=\delta(a_1)b_1 +a_1 \tau(b_1)+\delta(b_1)a_1 + b_1\tau(a_1)$ for all $a_1,b_1\in \mathcal{T}$ and for some maps $\tau$ over $\mathcal{T}$ satisfying  $\tau(a_1b_1+b_1a_1)=\tau(a_1)b_1+a_1 \tau(b_1)+\tau(b_1)a_1+b_1\tau(a_1)$, is additive. Secondly, it is shown that a map $T$ on $\mathcal{T}$ satisfying $T(a_1b_1)=T(a_1)b_1=a_1T(b_1)$ for all $a_1,b_1\in \mathcal{T}$ is additive. Finally, we show that if a map $D$ over $\mathcal{T}$ satisfies $(m+n)D(a_1b_1)=2mD(a_1)b_1+2na_1D(b_1)$ for all $a_1,b_1\in \mathcal{T}$ and integers $m,n\geq 1$, then $D$ is additive.
KW  - Additivity
KW  - Jordan derivation
KW  - two-sided centralizer
KW  - $(m
KW  - n)$-derivation
KW  - triangular ring
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UR  - https://doi.org/10.24330/ieja.1488471
L1  - https://dergipark.org.tr/en/download/article-file/3949287
ER  -