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What (who) is cylindrical semigroup - definition

GENERALIZATION OF THE EXPONENTIAL FUNCTION

C0 semigroup; Strongly continuous semigroup; One-parameter semigroup; Diffusion semigroup; Mild solution

Monogenic semigroup

SEMIGROUP GENERATED BY A SINGLE ELEMENT

Cyclic semigroup; Periodic semigroup

In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups.

https://en.wikipedia.org/wiki/Monogenic_semigroup

Null semigroup

SEMIGROUP WITH AN ABSORBING ELEMENT, CALLED ZERO, IN WHICH THE PRODUCT OF ANY TWO ELEMENTS IS ZERO

Zero semigroup; Left zero semigroup; Right zero semigroup

In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of a semigroup is a left zero then the semigroup is called a left zero semigroup; a right zero semigroup is defined analogously.

https://en.wikipedia.org/wiki/Null_semigroup

Semigroup with involution

SEMIGROUP EQUIPPED WITH AN INVOLUTIVE ANTI-AUTOMORPHISM

Free semigroup with involution; Free monoid with involution; Monoid with involution; *-regular semigroup; *-semigroup; Free half group; Involutive monoid; Dyck congruence; Shamir congruence; Foulis semigroup; Baer *-semigroup

In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application "cancelling itself out", and the same interaction law with the binary operation as in the case of the group inverse. It is thus not a surprise that any group is a semigroup with involution.

https://en.wikipedia.org/wiki/Semigroup_with_involution

Wikipedia

C0-semigroup

In mathematics, a C₀-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.

Formally, a strongly continuous semigroup is a representation of the semigroup (R₊, +) on some Banach space X that is continuous in the strong operator topology. Thus, strictly speaking, a strongly continuous semigroup is not a semigroup, but rather a continuous representation of a very particular semigroup.

https://en.wikipedia.org/wiki/C0-semigroup