MathStructures
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2019-12-08T21:37:45-08:00MathStructures
http://mathv.chapman.edu/~jipsen/structures/
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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/html2019-11-17T16:42:01-08:00Peter Jipsenindex.html
http://mathv.chapman.edu/~jipsen/structures/doku.php/index.html?rev=1574037721&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. Knowledgeable readers are encouraged to add or correct information.
To enable the edit button on each page, use the Login link (above) to log in or create an account.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:text/html2019-06-15T06:34:32-08:00commutative_residuated_partially_ordered_monoids
http://mathv.chapman.edu/~jipsen/structures/doku.php/commutative_residuated_partially_ordered_monoids?rev=1560605672&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: This is a template.
If you know something about this class, click on the ``Edit text of this page'' link at the bottom and fill out this page.<b><i></i></b><b><i>Title</i></b><b>1</i></b>text/html2019-03-28T16:22:05-08:00semirings_with_zero
http://mathv.chapman.edu/~jipsen/structures/doku.php/semirings_with_zero?rev=1553815325&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: