Morita-like equivalence for fair semigroups

Yıl 2020, Cilt: 49 Sayı: 1, 19 - 29, 06.02.2020

Yang Li Hongxing Liu

https://doi.org/10.15672/HJMS.2018.648

Öz

In this paper, we mainly investigate Morita-like equivalence and Morita context for right fair semigroups. If two right fair semigroups $S$ and $T$ are Morita-like equivalent, that is, there is a category equivalence $F:US-Act\rightleftharpoons:UT-Act:G,$  we characterize the two functors $F$ and $G$ using $Hom$ functor and tense product functor. Also, we investigate Morita context for right fair semigroups and obtain equivalence between two right unitary act categories.

Anahtar Kelimeler

fair semigroup, Morita equivalence, Morita context, equivalence, functor

Kaynakça

• [1] G. Abrams, Morita equivalence for rings with local units, Commun. Algebra, 11, 801–837, 1983.
• [2] P.N. Ánh and L.Márki, Morita equivalence for rings without identity, Tsukuba J. Math. 11, 1–16, 1987.
• [3] B. Banaschewski, Functors into categories of M-sets, Abh. Math. Sem. Univ. Ham- burg, 38, 49–64, 1972.
• [4] K.R. Fuller, Density and equivalence, J. Algebra 29, 528–550, 1974.
• [5] J.L. García and L.Marín, Rings having a Morita-like equivalence, Commun. Algebra, 27, 665–680, 1999.
• [6] J.M. Howie, Fundamentals of semigroup theory, Clarendon press, Oxford, 1995.
• [7] M. Kilp, U. Knauer and A.V. Mikhalev, Monoids Acts and Categories, Degruyter Expositions in Mathematics, 2000.
• [8] U. Knauer, Projectivity of acts and Morita equivalence of monoids, Semigroup Forum 3, 359–370, 1972.
• [9] V. Laan and L. Márki, Strong Morita equivalence of semigroups with local units, J. Pure Appl. Algebra, 215, 2538–2546, 2011.
• [10] V. Laan and L. Márki, Morita invariants for semigroups with local units, Monatsh. Math. 166, 441–451, 2012.
• [11] V. Laan and L. Márki, Fair semigroups and Morita equivalence, Semigroup Forum, 92, 633–644, 2016.
• [12] M.V. Lawson, Morita equivalence of semigroups with local units, J. Pure Appl. Alge- bra 215, 455–470, 2011.
• [13] H. Liu, Morita equivalence based on Morita context for arbitrary semigroups, Hacet. J. Math. Stat. 45 (4), 1083–1090, 2016.
• [14] B.Y. Ouyang and W.T. Tong, Morita context and Morita-like equivalence for the xst-rings, Acta Math. Sinica (English Series), 19, 371–380, 2003.
• [15] B.Y. Ouyang, L.R. Zhou and W.T. Tong, Characterizations of Morita-like Equiva- lences for right xst-rings, Algebra Colloquium, 14, 85–95, 2007.
• [16] S. Talwar, Morita equivalence for semigroups, J. Aust. Math. Soc. (Series A), 59, 81–111, 1995.
• [17] Y.H. Xu, K.P. Shum and R.F. Turner-Smith, Morita-like equivalence of infinite matrix subrings, J. Algebra, 159, 423–435, 1993.