[{"word":"algebra","phonetic":"/ˈæl.dʒɪ.bɹə/","phonetics":[{"text":"/ˈæl.dʒɪ.bɹə/","audio":""},{"text":"/ˈæl.dʒə.bɹə/","audio":"https://api.dictionaryapi.dev/media/pronunciations/en/algebra-us.mp3","sourceUrl":"https://commons.wikimedia.org/w/index.php?curid=1769831","license":{"name":"BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"}}],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.","synonyms":[],"antonyms":[]},{"definition":"The surgical treatment of a dislocated or fractured bone. Also : a dislocation or fracture.","synonyms":[],"antonyms":[]},{"definition":"The study of algebraic structures.","synonyms":[],"antonyms":[]},{"definition":"A universal algebra.","synonyms":[],"antonyms":[]},{"definition":"An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.","synonyms":["algebra over a field","algebra over a ring"],"antonyms":[]},{"definition":"A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).","synonyms":["field of sets"],"antonyms":[]},{"definition":"One of several other types of mathematical structure.","synonyms":[],"antonyms":[]},{"definition":"A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.","synonyms":[],"antonyms":[]}],"synonyms":["algebra over a field","algebra over a ring","field of sets"],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/algebra"]}]