Results 21 to 30 of about 73 (42)

On Po-injective and Po-surjective Wreath Product of Pomonoids

European Journal of Pure and Applied Mathematics
Let $R$  and $S$ be pomonoids and $_{R}{A}$ be a left $R$-poset. The wreath product of the pomonoids $R$  and $S$ by $_{R}{A}$  is defined as the pomonoid $T~=~R \times F(A, S)$ While, the wreath product $_TC$ of the left $R$-poset $_{R}{A}$ with the left $S$-poset $_{S}{B}$ over the pomonoid $T= R \times F(A, S)$ is the left $T$-poset ${_T C}= {_R A ...
Bana Al Subaiei, Ahlam Almulhim, Aftab Shah, Syed Ul Haq   +3 more
openaire   +1 more source

Every BCK-algebra is a set of residuables in an integral pomonoid

Journal of Algebra, 1988
It is shown that every BCK-algebra is isomorphic to a sub-algebra of the residuation-reduct of some integral commutative monoid with residuation. This result can be easily derived from embedding theorems of \textit{H. Ono} and \textit{Y. Komori} [J. Symb. Logic 50, 169-201 (1985; Zbl 0583.03018)] and \textit{M. Pałasiński} [An embedding theorem for BCK-
openaire   +1 more source

On Free Products and Amalgams of Pomonoids [PDF]

Communications in Algebra, 2016
The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and
Bana Al Subaiei, James Renshaw
exaly   +11 more sources

On the Coextension of Cut-Continuous Pomonoids [PDF]

Order, 2018
A partially ordered monoid, or pomonoid, is a monoid endowed with a compatible partial order, a pomonoid ia called cut-continuous if the product \(\cdot\) is separately cut-continuous, that is, the sets \(\{z : y\cdot z\leq x\}\) and \(\{z : z\cdot y \leq x\}\) are cuts for any \(x, y\in L.\) cut-continuous pomonoids are generalization of residuated ...
Jan Paseka, Thomas Vetterlein, David Kruml   +2 more
exaly   +5 more sources

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Perfection for pomonoids

Semigroup Forum, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victoria Gould
exaly   +3 more sources

ON COMMUTATIVE RESIDUAL POMONOIDS

Demonstratio Mathematica, 1998
Summary: We prove the following results: Commutative residual pomonoids with the identity as a maximal element are categorically equivalent to BCI-algebras with condition (S); commutative residual pomonoids with the identity as the greatest element, commutative implicative semigroups, and BCK-algebras with condition (S) are categorically equivalent to ...
exaly   +2 more sources

Representations of zero-cancellative pomonoids

Mathematica Slovaca, 2014
Abstract Several familiar results on representations of MV-algebras shape the idea that the use of solving systems of linear equations can be studied also in the setting of zero-cancellative commutative pomonoids. This paper investigates this idea and shows that for the class of linearly representable zero-cancellative commutative ...
Jan Paseka
exaly   +2 more sources

On zigzag theorem for commutative pomonoids and certain closed and absolutely closed monoids and pomonoids

Beitrage Zur Algebra Und Geometrie, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aftab Shāh
exaly   +3 more sources

On the homological classification of pomonoids: Clifford pomonoids

Semigroup Forum, 2014
The author characterizes Clifford pomonoids all of whose Rees factor \(S\)-posets satisfy property \((P_w)\), which in the row of so-called flatness properties lies between projective and po-flat. Clifford pomonoid (the author does not use this term) means a pomonoid which as a monoid is a Clifford semigroup.
exaly   +3 more sources

Varieties of Commutative Residuated Integral Pomonoids and Their Residuation Subreducts

Journal of Algebra, 1997
Let \(\langle A;\oplus ,0,\leq \rangle\) be a commutative (dually) integral partially ordered monoid whose identity \(0\) is the least element of \(\langle A,\leq \rangle\), where \(\leq\) is a partial order compatible with the monoid operation \(\oplus\) in the sense that \(a\oplus b\leq c\oplus d\) whenever \(a\leq c\) and \(b\leq d\).
Blok, Willem J., Raftery, James G.
exaly   +3 more sources