Khosravi, R., Sedaghatjoo, M. (2016). Properties of products for flatness in the category of $S$-posets. Categories and General Algebraic Structures with Applications, 5(1), 131-152.
Roghaieh Khosravi; Mojtaba Sedaghatjoo. "Properties of products for flatness in the category of $S$-posets". Categories and General Algebraic Structures with Applications, 5, 1, 2016, 131-152.
Khosravi, R., Sedaghatjoo, M. (2016). 'Properties of products for flatness in the category of $S$-posets', Categories and General Algebraic Structures with Applications, 5(1), pp. 131-152.
Khosravi, R., Sedaghatjoo, M. Properties of products for flatness in the category of $S$-posets. Categories and General Algebraic Structures with Applications, 2016; 5(1): 131-152.
Properties of products for flatness in the category of $S$-posets
1Department of Mathematics, Fasa University, Fasa, Iran.
2Department of Mathematics, College of Science, Persian Gulf University, Bushehr, Iran.
Abstract
This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condition $(PWP)$. Finally, we investigate pomonoids over which products of right $S$-posets transfer an arbitrary flatness property, projectivity, freeness, and regularity to their components.
[1] S. Bulman-fleming, D. Gutermuth, A. Glimour, and M. Kilp, Flatness properties of S-posets, Comm. Algebra 34(4) (2006), 1291-1317. [2] S. Bulman-Fleming and A. Gilmour, Flatness properties of diagonal acts over monoids, Semigroup Forum 79(2) (2009), 298-314. [3] S. Bulman-Fleming and K. McDowell, Coherent monoids, In: Almeida, J., et al., eds. Latices, Semigroups and Universal Algebra. New York: Plenum Press, (1990). [4] S. Bulman-Fleming, Products of projective S-system, Comm. Algebra 19(3) (1991), 951-964. [5] S. Bulman-Fleming and M. Mahmoudi, The category of S-posets, Semigroup Forum 71(3) (2005), 443-461. [6] S.M. Fakhruddin, Absolute flatness and amalgams in pomonoids, Semigroup Forum 33 (1986), 15-22. [7] S.M. Fakhruddin, On the category of S-posets, Acta Sci. Math. (Szeged) 52 (1988), 85-92. [8] A. Golchin and P. Rezaei, Subpullbacks and flatness properties of S-posets, Comm. Algebra 37(6) (2009), 1995-2007. [9] R. Khosravi, On direct products of S-posets satisfying flatness properties, Turk. J. Math. 38 (2014), 79-86. [10] X.L. Liang and Y.F. Luo, On Condition (PWP)w for S-posets, Turk. J. Math. 39 (2015), 795-809. [11] X.L. Liang and Y. Luo, Subpullbacks and coproducts of S-posets, Categ. General Alg. Struct. Appl. 3(1) (2015), 1-20. [12] L. Nouri, A. Golchin, and H. Mohammadzadeh, On Properties of Product acts over monoids, Comm. Algebra 43(5) (2015), 1854-1876. [13] H.S. Qiao and H.C. Wen, On a generalizations of principally weakly po-flat poset, J. Shandong. Univ. 50(12) (2015), 1571-9352.
[14] M. Sedaghatjoo, R. Khosravi, and M. Ershad, Principaly weakly and weakly coherent monoids, Comm. Algebra 37(12) (2009), 4281-4295. [15] X. Shi, On flatness properties of cyclic S-posets, Semigroup Forum 77(2) (2008), 248-266. [16] X. Shi, Strongly flat and po-flat S-posets, Comm. Algebra 33(12) (2005), 4515-4531. [17] X. Shi, Z. Liu, F. Wang, and S. Bulman-Fleming, Indecomposable, projective, and flat S-posets, Comm. Algebra 33(1) (2005), 235-251.