generic_alg_cats http://www.openmath.org/cd/generic_alg_cats.ocd 2005-04-01 experimental 2002-06-17 0 0 algebraic_cats logic1 meta_cats set1 A CD of generic algebraic categories. This CD holds information relating to the heirarchical sturcture of the algebraic category system. monoid This Symbol represents the generic category of monoid. A monoid is a groupoid Abelian_monoid This Symbol represents the generic category of Abelian monoid. An Abelian monoid is a monoid ordered_monoid This Symbol represents the generic category of ordered monoid. An ordered monoid is a monoid ordered_Abelian_monoid This Symbol represents the generic category of ordered Abelian monoid. An ordered Abelian monoid is an Abelian monoid An ordered Abelian monoid is an ordered monoid groupoid This Symbol represents the generic category of groupoid. semigroup This Symbol represents the generic category of semigroup. A semigroup is a groupoid Abelian_semigroup This Symbol represents the generic category of Abelian semigroup. An Abelian semigroup is a semigroup group This Symbol represents the generic category of group. A group is a monoid ordered_group This Symbol represents the generic category of ordered group. An ordered group is a group Abelian_group This Symbol represents the generic category of Abelian group. An Abelian group is a group ordered_Abelian_group This Symbol represents the generic category of ordered Abelian group. An ordered Abelian group is an Abelian group An ordered Abelian group is an ordered group ringoid This symbol represents the generic category of ringoid. ring This Symbol represents the generic category of ring. A ring is a ringoid A ring is a group under addition A ring is a semigroup under multiplication ordered_ring This Symbol represents the generic category of ordered ring. An ordered ring is a ring non_commutative_ring This Symbol represents the generic category of non-commutative ring. A non-commutative ring is a ring Euclidean_domain This Symbol represents the generic category of Euclidean domain. A Euclidean domain is a ring field This Symbol represents the generic category of field. A field is an Abelian group under + A field is a ring integral_domain This Symbol represents the generic category of integral domain. An integral domain is a ring