Regular

The term regular can mean normal or in accordance with rules. It may refer to:

Organizations

Regular Army for military usage
Regular clergy, members of a religious order subject to a rule of life
Regular Force for usage in the Canadian Forces
Regular Masonic jurisdictions, or regularity, refers to the constitutional mechanism by which Freemasonry Grand Lodges or Grand Orients give one another mutual recognition

Regular Show, an animated television series
The Regular Guys, a radio morning show based out of Atlanta, Georgia
Regular Joe, the second studio album by American country music artist Joe Diffie

Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language
- Regular verb
Regular script, the newest of the Chinese script styles

There is an extremely large number of unrelated notions of "regularity" in mathematics.

(See also the geometry section for notions related to algebraic geometry.)

Regular category, a kind of category that has similarities to both Abelian categories and to the category of sets
Regular element (disambiguation), certain kinds of elements of an algebraic structure
Regular extension of fields
Regular ideal (multiple definitions)
Regular monomorphisms and regular epimorphisms, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms
Regular numbers, numbers which evenly divide a power of 60
Regular p-group, a concept capturing some of the more important properties of abelian p-groups, but general enough to include most "small" p-groups
Regular prime, a prime number p > 2 that does not divide the class number of the p-th cyclotomic field
The regular representation of a group G, the linear representation afforded by the group action of G on itself
Regular ring, a ring such that all its localizations have Krull dimension equal to the minimal number of generators of the maximal ideal
von Neumann regular ring, or absolutely flat ring (unrelated to the previous sense)
Regular semigroup, related to the previous sense
*-regular semigroup
Regular chains in computer algebra
Regular semi-algebraic systems in computer algebra

Regular functions, functions that are analytic and single-valued (unique) in a given region
Regular measure, a measure for which every measurable set is "approximately open" and "approximately closed"
Borel regular measure
The regular part of a Laurent series, the series of terms with positive powers
Regular singular points in theory of ordinary differential equations where the growth of solutions is bounded by an algebraic function
Cauchy-regular function, a continuous function between metric spaces which preserves Cauchy sequences
Regularity, the degree of differentiability of a function
Regularity conditions arise in the study of first class constraints in Hamiltonian mechanics
Regularity of an elliptic operator
Regular matrix (disambiguation)

Regular code, an algebraic code with a uniform distribution of distances between codewords
Regular graph, a graph such that all the degrees of the vertices are equal
Szemerédi regularity lemma, some random behaviors in large graphs
Regular map (graph theory), a symmetric tessellation of a closed surface
Regular expression, a type of pattern describing a set of strings in computer science
Regular language, a formal language recognizable by a finite state automaton (related to the previous sense)
Regular tree grammar
Regular matroid, a matroid which can be represented over any field
Regular paperfolding sequence, also known as the dragon curve sequence
Regular algebra, or Kleene algebra

Regular curves
Regular map (algebraic geometry), a map between varieties given by polynomials
Regular point of a differentiable map, a point at which a map is a submersion
Regular point of an algebraic variety, a point at which a variety is non-singular
Regular surface in algebraic geometry
Castelnuovo–Mumford regularity of a coherent sheaf
Regular polygons, polygons with all sides and angles equal
Regular polyhedrons and regular polytopes, generalizations of the previous sense to higher dimensions
Regular skew polyhedron
Regular grid, a tesselation of Euclidean space by congruent bricks
Closed regular sets in solid modeling

Regular cardinal, a cardinal number that is equal to its cofinality
Axiom of Regularity, also called the Axiom of Foundation, an axiom of set theory asserting the non-existence of certain infinite chains of sets
Regular modal logic
Partition regularity

Regular conditional probability, a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions
Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive

Regular (or $T_{3}$ ) space, a topological space in which a point and a closed set can be separated by neighborhoods
Regular homotopy
Free regular set, a subset of a topological space that is acted upon disjointly under a given group action
Regular isotopy in knot theory, the equivalence relation of link diagrams that is generated by using the 2nd and 3rd Reidemeister moves only

Regular bowel movements, the opposite of constipation
Regular solutions in chemistry, solutions that diverge from the behavior of an ideal solution only moderately
Regular economy, an economy characterized by an excess demand function whose slope at any equilibrium price vector is non-zero

Regular character, a main character who appears more frequently and/or prominently than a recurring character
Regular customer, a person who visits the same restaurant, pub, store, or transit provider frequently
Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings
Regular footedness in boardsports, a stance in which the left foot leads
Regular division of the plane, a series of drawings by the Dutch artist M. C. Escher which began in 1936
The Regular Baptists, an 18th-century American and Canadian Baptist group
Regular moon, a natural satellite that has low eccentricity and a relatively close and prograde orbit