A binary operator symbol combining a plus sign with a square box, commonly used in algebraic structures and logic.
Examples
Direct sum of vector spaces
V \boxplus W = \{(v,w) : v \in V, w \in W\}
Direct sum of modules
M_1 \boxplus M_2 \boxplus M_3 = \bigoplus_{i=1}^3 M_i
Orthogonal direct sum of subspaces
\mathbb{R}^4 = V_1 \boxplus V_2 \text{ where } V_1 \perp V_2