MathStructures
http://mathv.chapman.edu/~jipsen/structures/
2020-01-26T01:18:56-08:00MathStructures
http://mathv.chapman.edu/~jipsen/structures/
http://mathv.chapman.edu/~jipsen/structures/lib/images/favicon.icotext/html2019-12-12T08:00:18-08:00Peter Jipsencommutative_residuated_partially_ordered_monoids
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_residuated_partially_ordered_monoids?rev=1576166418&do=diff
Commutative residuated partially ordered monoids
Abbreviation: CRPoMon
Definition
A <b><i>commutative residuated partially ordered monoid</i></b> is a residuated partially ordered monoid such that
is <b><i>commutative</i></b>:
Remark: These algebras are also known as <b><i>lineales</i></b>.<b><i>Lineales: Algebras and Categories in the Semantics of Linear Logic</i></b>text/html2019-12-10T17:29:00-08:00Peter Jipsenindex.html
http://mathv.chapman.edu/~jipsen/structures/doku.php/index.html?rev=1576027740&do=diff
Mathematical Structures
The webpages collected here list information about classes of
mathematical structures. The aim is to have a central place to check
what properties are known about these structures.
These pages are currently still under construction.text/html2019-11-30T12:19:59-08:00Peter Jipsenstone_algebras
http://mathv.chapman.edu/~jipsen/structures/doku.php/stone_algebras?rev=1575145199&do=diff
Stone algebras
Abbreviation: StAlg
Definition
A <b><i>Stone algebra</i></b> is a distributive p-algebra such that
,
Morphisms
Let and be Stone algebras. A morphism from to is a function that is a
homomorphism:
, , , ,
Examples
Example 1:text/html2019-11-17T16:31:29-08:00Peter Jipsencommutative_idempotent_involutive_residuated_lattices - created
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_idempotent_involutive_residuated_lattices?rev=1574037089&do=diff
Commutative idempotent involutive FL-algebras
Abbreviation: CIdInFL
Definition
A <b><i>commutative idempotent involutive FL-algebra</i></b> or <b><i>commutative idempotent involutive residuated lattice</i></b> is a structure of type such that<b><i>involution</i></b><b><i>commutative involutive FL-algebra</i></b><b><i>commutative involutive residuated lattice</i></b><b><i>Residuated frames with applications</i></b>text/html2019-11-17T16:30:10-08:00Peter Jipsencommutative_involutive_fl-algebras
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_involutive_fl-algebras?rev=1574037010&do=diff
Commutative involutive FL-algebras
Abbreviation: CInFL
Definition
A <b><i>commutative involutive FL-algebra</i></b> or <b><i>commutative involutive residuated lattice</i></b> is a structure of type such that
is a lattice
is a commutative monoid<b><i>involution</i></b><b><i>commutative involutive FL-algebra</i></b><b><i>commutative involutive residuated lattice</i></b><b><i>Residuated frames with applications</i></b>text/html2019-11-17T16:27:06-08:00Peter Jipsencommutative_idempotent_integral_involutive_fl-algebras - created
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_idempotent_integral_involutive_fl-algebras?rev=1574036826&do=diff
Commutative idempotent involutive FL-algebras
Abbreviation: CIdInFL
Definition
A <b><i>commutative idempotent involutive FL-algebra</i></b> or <b><i>commutative idempotent involutive residuated lattice</i></b> is a structure of type such that<b><i>involution</i></b><b><i>commutative involutive FL-algebra</i></b><b><i>commutative involutive residuated lattice</i></b><b><i>Residuated frames with applications</i></b>text/html2019-11-17T13:33:27-08:00Peter Jipsenbasic_logic_algebras
http://mathv.chapman.edu/~jipsen/structures/doku.php/basic_logic_algebras?rev=1574026407&do=diff
Basic logic algebras
Abbreviation: BLA
Definition
A <b><i>basic logic algebra</i></b> or <b><i>BL-algebra</i></b> is a structure such that
is a
bounded lattice
is a commutative monoid
gives the residual of :
prelinearity:
BL:
Remark:
The BL identity implies that the lattice is distributive.<b><i>basic logic algebra</i></b>text/html2019-10-13T18:50:41-08:00quantales
http://mathv.chapman.edu/~jipsen/structures/doku.php/quantales?rev=1571017841&do=diff
Quantales
Abbreviation: Quant
Definition
A <b><i>quantale</i></b> is a structure of type such that
is a complete semilattice with ,
is a semigroup, and
distributes over : and
Remark: In particular, distributes over the empty join, so .<b><i>Title</i></b><b>1</i></b>text/html2019-07-20T10:48:42-08:00distributive_residuated_lattices
http://mathv.chapman.edu/~jipsen/structures/doku.php/distributive_residuated_lattices?rev=1563644922&do=diff
Distributive residuated lattices
Abbreviation: DRL
Definition
A <b><i>distributive residuated lattice</i></b> is a residuated lattice such that
are distributive:
Remark:
Morphisms
Let and be distributive residuated lattices. A
morphism from to is a function
that is a homomorphism:text/html2019-06-16T03:56:48-08:00commutative_residuated_lattices
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_residuated_lattices?rev=1560682608&do=diff
Commutative residuated lattices
Abbreviation: CRL
Definition
A <b><i>commutative residuated lattice</i></b> is a residuated lattice such that
is commutative:
Remark:
Morphisms
Let and be commutative residuated lattices. A
morphism from to is a function
that is a homomorphism: