Antonym of the word nullity in the context of Boolean algebra

Question

Depending on what axioms one uses to define a Boolean algebra, one result one can often show for a Boolean algebra $(S,+,*)$ is that for all $x \in S$, $x + 1 = 1$ and $x * 0 = 0$. I have seen some textbooks and authors use the word "nullity" to describe the second statement. However, I don't remember a one word used to describe or explain the first statement. The closest word I can think of is "totality" but perhaps there is a more accurate term?

Answer 1

Both of these are sometimes called "dominant laws". The fact that $x+1=1$ is additive dominance and $x*0=0$ is multiplicative dominance. Alternatively you can consider $x+1=1$ to be additive nullity.

Answer 2

Well, in a ring, the property $x\cdot 0=0$ is referred to as absorption. In this way, both of the Boolean laws are ''absorption'' laws.