Ben Amor, Mohamed Amine The Riesz tensor product of \(d\)-algebras. (English) Zbl 07462250 Quaest. Math. 44, No. 11, 1553-1562 (2021). Summary: In this work we prove that the Riesz tensor product of two Archimedean \(d\)-algebras is again a \(d\)-algebra. MSC: 06F25 Ordered rings, algebras, modules 15A69 Multilinear algebra, tensor calculus Keywords:tensor product; \(d\)-algebras; Riesz algebras PDF BibTeX XML Cite \textit{M. A. Ben Amor}, Quaest. Math. 44, No. 11, 1553--1562 (2021; Zbl 07462250) Full Text: DOI OpenURL References: [1] Azouzi, Y.; Ben Amor, M. A.; Jaber, J., The tensor product of f -algebras, Quaest. Math, 41, 3, 359-369 (2018) · Zbl 1400.46003 [2] Bernau, S. J.; Huijsmans, C. B., Almost f -algebras and d-algebras, Math. Proc. Cambridge Philos. Soc., 107, 2, 287-308 (1990) · Zbl 0707.06009 [3] Birkhoff, Garrett [4] Birkhoff, G.; Pierce, R. S., Lattice-ordered rings, An. Acad. Brasil. Ci., 28, 41-69 (1956) · Zbl 0070.26602 [5] Boulabiar, K., Representation theorems for d-multiplications on archimedean unital f -rings, Communications in Algebra, 32, 10, 3955-3967 (2004) · Zbl 1060.06023 [6] Boulabiar, K., Recent trends on order bounded disjointness preserving operators, Irish Math. Soc. Bull, 62, 43-69 (2008) · Zbl 1188.47032 [7] Bu, Q.; Buskes, G.; Kusraev, A. G., Bilinear maps on products of vector lattices: a survey, In: Positivity, Trends Math, 97-126 · Zbl 1149.46007 [8] Buskes, G. J.H. M.; Wickstead, A. W., Tensor products of f -algebras, Mediterr. J. Math, 14, 2 (2017) · Zbl 1378.06017 [9] Conrad, P. F.; Diem, J. E., The ring of polar preserving endomorphisms of an abelian lattice-ordered group, Illinois J. Math, 15, 222-240 (1971) · Zbl 0213.04002 [10] Fremlin, D. H., Tensor products of Archimedean vector lattices, Amer. J. Math, 94, 777-798 (1972) · Zbl 0252.46094 [11] Grobler, J. J.; Labuschagne, C. C.A., The tensor product of Archimedean or- dered vector spaces, Math. Proc. Cambridge Philos. Soc, 104, 2, 331-345 (1988) · Zbl 0663.46006 [12] Boulabiar, K., An f -algebra approach to the Riesz tensor product of Archimedean Riesz spaces, Quaestiones Math, 12, 4, 425-438 (1989) · Zbl 0728.46049 [13] Kudlácek, Václav, On some types of l-rings, Sb. Vysoké. Učení Tech. Brno, 1962, 1-2, 179-181 (1962) · Zbl 0133.27201 [14] Kusraev, A. G.; Tabuev, S. N., On disjointness preserving bilinear operators, Vladikavkazsk. Mat. Zh, 6, 1, 58-70 (2004) · Zbl 1094.47514 [15] Kusraev, A. G.; Tabuev, S. N., On a multiplicative representation of bilinear operators, Sibirsk. Mat. Zh, 49, 2, 357-366 (2008) · Zbl 1164.47335 [16] Luxemburg, W.A.J., Some aspects of the theory of Riesz spaces, University of Arkansas Lecture Notes in Mathematics, Vol. 4, University of Arkansas, Fayetteville, Ark., 1979. · Zbl 0431.46003 [17] Luxemburg, W. A.J.; Zaanen, A. C., Riesz Spaces I (1971), North-Holland Publishing Co.: North-Holland Publishing Co., Amsterdam/London · Zbl 0231.46014 [18] Meyer, M., Le stabilateur d’un espace vectoriel réticulé, C.R. Acad. Sci. Paris, 283, 249-250 (1976) · Zbl 0334.46010 [19] Meyer-Nieberg, P., Banach Lattices (1991), Springer-Verlag: Springer-Verlag, Berlin/Heidelberg/New York [20] Schaefer, H. H., Banach lattices, Banach Lattices and Positive Operators, 46-153 (1974), Springer: Springer, Berlin/Heidelberg [21] Schaefer, H. H., Aspects of Banach lattices, In: Studies in functional analysis, MAA Stud. Math, 21, 158-221 [22] Zaanen, A. C., Riesz spaces II, 30 (1983), North- Holland Publishing Co.: North- Holland Publishing Co., Amsterdam · Zbl 0519.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.