Results 1 to 10 of about 136 (51)

On homological classification of pomonoids by GP-po-flatness of S-posets

Open Mathematics, 2016
In this paper, we introduce GP-po-flatness property of S-posets over a pomonoid S, which lies strictly between principal weak po-flatness and po-torsion freeness.
Xingliang Liang, Yanfeng Luo
exaly   +3 more sources

Epimorphisms Amalgams and Po-Unitary Pomonoids

Axioms
This paper proves that the special pomonoid amalgam with a quasi po-unitary or almost po-unitary core U is strongly poembeddable. The techniques used to establish these results involve Isbell’s zigzag theorem and its descriptions in terms of the pomonoid
Aftab Hussain Shāh, Bana Al Subaiei, Al Subaiei Bana   +2 more
exaly   +4 more sources

Characterization of Pomonoids by Properties of I-Regular S-Posets

Mathematics
In 2005, Shi defined I-regular S-posets and used this concept to characterize PP-pomonoids and po-cancellable pomonoids. In this paper, we continued the development of the homological classification of pomonoids by using the I-regularity of S-posets ...
Tingting Zhao
exaly   +4 more sources

Erratum to “On homological classification of pomonoids by regular weak injectivity properties of S-posets”

Open Mathematics, 2009
The original version of the article was published in Central European Journal of Mathematics, 2007, 5(1), 181–200, DOI: 10.2478/s11533-006-0036-3. Unfortunately, the original version of this article contains a mistake: in Theorem 5.2 only conditions (i ...
Valdis Laan
exaly   +3 more sources

On the Coextension of Cut-Continuous Pomonoids

Order, 2018
We introduce cut-continuous pomonoids, which generalise residuated posets. The latter’s defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each ...
David Kruml, Jan Paseka, Thomas Vetterlein   +2 more
exaly   +2 more sources

ON REGULAR PRIME INJECTIVITY OF S-POSETS [PDF]

Journal of Algebraic Systems, 2021
In this paper, we define the notion of regular prime monomorphism for $S$-posets over a pomonoid $S$ and investigate some categorical properties including products, coproducts and pullbacks.
H. Rasouli, Gh. R. Moghaddasi, N. Sarvghad   +2 more
doaj   +2 more sources

Representations of zero-cancellative pomonoids

Mathematica Slovaca, 2014
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.
Jan Paseka
exaly   +2 more sources

Varieties of Commutative Residuated Integral Pomonoids and Their Residuation Subreducts

Journal of Algebra, 1997
The notion of residuation can already be found in Dedekind’s work on modules, and it has played an important role in ideal theory ever since. If R is a commutative ring with 1, and I and J are ideals of R then the residual of I with respect to J is the ...
W. J. Blok, J. Raftery
exaly   +2 more sources

On a generalization of I-regularity

Open Mathematics
Let SS be a pomonoid. The projectivity and strong flatness of right SS-posets have been central topics in the homological classification of pomonoids in recent decades. In 2005, Shi et al. introduced II-regular SS-posets and proved that all its cyclic SS-
Qiao Husheng, Feng Leting
doaj   +2 more sources

ON COMMUTATIVE RESIDUAL POMONOIDS

Demonstratio Mathematica, 1998
Early in 1963, L.Fuchs [5] systematically investigated the theory of residual pomonoids. In [12], A. Wroñski first studied the relationship between BCK-algebras and commutative residual pomonoids, and obtained that every BCK-algebra is isomorphic to the ...
J. Meng
exaly   +2 more sources