http://math.chapman.edu/~jipsen/structures/ 2013-06-19T00:00:37-07:00 http://math.chapman.edu/~jipsen/structures/ http://math.chapman.edu/~jipsen/structures/lib/images/favicon.ico text/html 2013-06-06T21:38:43-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/idempotent_semirings_with_zero?rev=1370579923&do=diff Idempotent semirings with zero Abbreviation: ISRng Definition An <b><i>idempotent semiring with zero</i></b> is a semirings with zero such that is idempotent: Morphisms Let and be idempotent semirings with zero. A morphism from to is a function that is a homomorphism: text/html 2013-06-06T21:34:11-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/idempotent_semirings_with_identity_and_zero?rev=1370579651&do=diff Idempotent semirings with identity and zero Abbreviation: ISRng Definition An <b><i>idempotent semiring with identity and zero</i></b> is a semirings with identity and zero such that is idempotent: Morphisms Let and be idempotent semirings with identity and zero. A morphism from to is a function that is a homomorphism: text/html 2013-06-06T21:31:47-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/semirings_with_identity?rev=1370579507&do=diff Semirings with identity Abbreviation: SRng$_1$ Definition A <b><i>semiring with identity</i></b> is a structure of type such that is a commutative semigroup is a monoid distributes over : , Morphisms Let and be semirings with zero. A morphism from to is a function that is a homomorphism: text/html 2013-06-06T21:23:08-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/semirings_with_zero?rev=1370578988&do=diff Semirings with zero Abbreviation: SRng$_0$ Definition A <b><i>semiring with zero</i></b> is a structure of type such that is a commutative monoid is a semigroup is a zero for : , distributes over : , Morphisms Let and be semirings with zero. A morphism from to is a function that is a homomorphism: text/html 2013-06-06T21:18:47-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/semirings?rev=1370578727&do=diff Semirings Abbreviation: SRng Definition A <b><i>semiring</i></b> is a structure of type such that is a semigroup is a commutative semigroup distributes over : , Morphisms Let and be semirings. A morphism from to is a function that is a homomorphism: text/html 2013-06-06T21:16:28-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/idempotent_semirings?rev=1370578588&do=diff Idempotent semirings Abbreviation: ISRng Definition An <b><i>idempotent semiring</i></b> is a semiring such that is idempotent: Morphisms Let and be idempotent semirings. A morphism from to is a function that is a homomorphism: , text/html 2013-06-01T14:36:04-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/equations?rev=1370122564&do=diff Syntax | Terms | Equations | Horn formulas | Universal formulas | First-order formulas | Theories Here we list equations, with the shorter term on the right (if possible). 1 trivial equations: one-element algebras 2 identity operation: 3 involutive operation: 4 inverse operations: 5 inside absorption: 6 outside absorption: 7 order- operation: 8 -idempotent 9 constant operations: 10 left projection: right projection: 11 idempo… text/html 2013-04-13T13:37:03-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/generalized_bl-algebras?rev=1365885423&do=diff Generalized BL-algebras Abbreviation: GBL Definition A <b><i>generalized BL-algebra</i></b> is a residuated lattice such that , Morphisms Let and be generalized BL-algebras. A morphism from to is a function that is a homomorphism: , , , , , text/html 2013-03-14T17:17:56-07:00 Peter Jipsen http://math.chapman.edu/~jipsen/structures/doku.php/modular_lattices?rev=1363306676&do=diff Modular lattices Abbreviation: MLat Definition A <b><i>modular lattice</i></b> is a lattice that satisfies the <b><i>modular identity</i></b>: Definition A <b><i>modular lattice</i></b> is a lattice that satisfies the <b><i>modular law</i></b>: <b><i>modular lattice</i></b><b><i>\Uber die von drei Moduln erzeugte Dualgruppe</i></b><b>53</i></b><b><i>Free modular lattices</i></b><b>261</i></b><b><i>On the word problem for the modular lattice with four free generators</i></b><b>265</i>… text/html 2012-10-01T14:03:44-07:00 Josh Flynn http://math.chapman.edu/~jipsen/structures/doku.php/vector_spaces?rev=1349125424&do=diff Vector spaces Abbreviation: FVec Definition A <b><i>vector space</i></b> over a field is a structure such that is an abelian groups scalar product distributes over vector addition: is the identity map: scalar product distributes over scalar addition: <b><i>scalar multiplication by </i></b><b><i>linear</i></b>