{"id":13766,"date":"2014-12-15T13:46:00","date_gmt":"2014-12-15T12:46:00","guid":{"rendered":"https:\/\/rafen.app\/uncategorized\/algebra\/"},"modified":"2023-02-07T18:51:54","modified_gmt":"2023-02-07T17:51:54","slug":"algebra","status":"publish","type":"post","link":"https:\/\/raf.edu.rs\/en\/subjects\/algebra\/","title":{"rendered":"Algebra"},"content":{"rendered":"<h5>Objectives and outcomes<\/h5>\n<p>Acquiring general and professional knowledge of algebra. Students will acquire important concepts and knowledge of both general algebra and various types of algebraic structures. General algebra &#8211; notion of algebraic structure, algebraic law, homomorphism of algebraic structures, congruence, quotient structure, the result of algebraic structures. Special algebraic structures \u2013 semigroup, monoid, group, ring, module over a ring, field, network, Boolean algebra. The emphasis is put on basic theorems of group theory.<\/p>\n<p>\u00a0<\/p>\n<h5>Lectures<\/h5>\n<p>Algebraic operations. Algebraic laws. External operation. Sub-operation. Algebraic structure. Substructure. Homomorphisms. Types of homomorphisms. Compositions of homomorphisms. Direct and inverse images. Isomorphism as an equivalence relation on the classes of algebraic structures. Congruences. Quotient structures. Natural homomorphism. Kernel of a homomorphism. Homomorphism decomposition theorem. Direct product of algebras. Groupoids. Semigroups. Regularity of elements in semigroups. Monoids. Invertibility of elements in monoids. Submonoids. Monoid homomorphisms. Groups. Subgroups. Cosets of a subgroup. Lagrange\u2019s theorem. Group homomorphisms. Order of an element. Cyclic groups. Theorems on cyclic groups. Normal subgroups. Correspondence between normal subgroups and congruences. Rings. Examples. Modules over rings. Fields. Examples. A network as a partially ordered set and as an algebraic structure. Complete lattices. Boolean algebra. Trivial and two-element Boolean algebra.<\/p>\n<h5>Practical classes<\/h5>\n<p>Computational exercises, solving tasks that follow the units covered in lectures.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Objectives and outcomes Acquiring general and professional knowledge of algebra. Students will acquire important concepts and knowledge of both general algebra and various types of algebraic structures. General algebra &#8211; notion of algebraic structure, algebraic &#8230; <a title=\"Algebra\" class=\"read-more\" href=\"https:\/\/raf.edu.rs\/en\/subjects\/algebra\/\" aria-label=\"More on Algebra\">Read more<\/a><\/p>\n <a href=\"https:\/\/raf.edu.rs\/en\/subjects\/algebra\/\" class=\"more-link\" title=\"Read more\">Read more<\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[199],"tags":[],"class_list":["post-13766","post","type-post","status-publish","format-standard","hentry","category-subjects"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Algebra - School of Computing<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/raf.edu.rs\/en\/subjects\/algebra\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algebra - School of Computing\" \/>\n<meta property=\"og:description\" content=\"Objectives and outcomes Acquiring general and professional knowledge of algebra. Students will acquire important concepts and knowledge of both general algebra and various types of algebraic structures. General algebra &#8211; notion of algebraic structure, algebraic ... 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