# De Morgan algebra

## English

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### Etymology

Named after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.

### Noun

De Morgan algebra (plural De Morgan algebras)

1. (algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.
• 1980, H. P. Sankappanavar, A Characterization of Principal Congruences of De Morgan Algebras and its Applications, A. I. Arruda, R. Chuaqui, N. C. A. Da Costa (editors), Mathematical Logic in Latin America: Proceedings of the IV Latin American Symposium on Mathematical Logic, page 341,
Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.
• 2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras, The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268,
By a topological de Morgan algebra we shall mean an abstract algebra ${\displaystyle (A,\land ,\lor ,\ ',l)}$ where ${\displaystyle (A,\land ,\lor ,l)}$ is a de Morgan algebra,
• 2009, George Rahonis, Chapter 12: Fuzzy Languages, Manfred Droste, Werner Kuich, Heiko Vogler (editors), Handbook of Weighted Automata, Springer, page 486,
If ${\displaystyle (L,\leq ,{^{-}})}$ is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then ${\displaystyle (L\langle \!\langle S\rangle \!\rangle ,\leq ,{^{-}})}$ constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every ${\displaystyle r\in L\langle \!\langle S\rangle \!\rangle }$ its negation ${\displaystyle {\overline {r}}\in L\langle \!\langle S\rangle \!\rangle }$ is defined by ${\displaystyle ({\overline {r}},s)={\overline {(r,s)}}}$ for every ${\displaystyle s\in S}$.