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Structure of relatively free dimonoids. (English) Zbl 1371.08006
A dimonoid is an algebra with two associative operations \(\vdash\), \(\dashv\) and with an identity \((x\vdash y)\dashv z= x\vdash (y\dashv z)\). The paper presents constructions of free dimonoids in the cases where one of the operations is a left (right) zero semigroup, a rectangular band, a normal (left, right) band etc. Constructions of free nilpotent, dinilpotent, abelian and some others diminoids are given. These constructions present canonical form of elements.

MSC:
08B20 Free algebras
08A30 Subalgebras, congruence relations
20M10 General structure theory for semigroups
08A05 Structure theory of algebraic structures
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[1] DOI: 10.1142/S0218196710005753 · Zbl 1245.17001 · doi:10.1142/S0218196710005753
[2] Boyd S. J., Proceedings of the Tennessee Topology Conference, Nashville, TN, USA, 1996 pp 33– (1997)
[3] Drouzy, M. (1986). La structuration des ensembles de semigroupes d’ordre 2, 3 et 4 par la relation d’interassociativit√©. Manuscript.
[4] DOI: 10.1007/3-540-45328-8_3 · doi:10.1007/3-540-45328-8_3
[5] DOI: 10.1007/s00233-006-0655-9 · Zbl 1122.20029 · doi:10.1007/s00233-006-0655-9
[6] DOI: 10.1007/s00233-002-0028-y · Zbl 1059.20056 · doi:10.1007/s00233-002-0028-y
[7] Gould M., Czechoslovak Math. J. 33 (1) pp 95– (1983)
[8] Hewitt E., Semigroups: Proceedings 1968 Wayne State U. Symposium on Semigroups pp 55– (1969)
[9] Kinyon M. K., J. Lie Theory 17 (4) pp 99– (2007)
[10] DOI: 10.1007/s11202-008-0026-8 · doi:10.1007/s11202-008-0026-8
[11] DOI: 10.1080/03081087.2012.686108 · Zbl 1273.17003 · doi:10.1080/03081087.2012.686108
[12] Koreshkov N. A., Izv. Vyssh. Uchebn. Zaved. Mat. 12 pp 34– (2008)
[13] Liu, K. A. (2004). A class of ring-like objects. Preprint, Available at: http://arxiv.org/abs/math/0411586v2.
[14] Loday J.-L., Ens. Math. 39 pp 269– (1993)
[15] DOI: 10.1007/3-540-45328-8_2 · doi:10.1007/3-540-45328-8_2
[16] DOI: 10.1090/conm/346/06296 · doi:10.1090/conm/346/06296
[17] DOI: 10.1081/AGB-120013311 · Zbl 1025.20042 · doi:10.1081/AGB-120013311
[18] DOI: 10.1007/s00233-004-0169-2 · Zbl 1095.20052 · doi:10.1007/s00233-004-0169-2
[19] DOI: 10.2478/BF02476006 · Zbl 1032.16032 · doi:10.2478/BF02476006
[20] DOI: 10.1007/s11202-009-0118-0 · doi:10.1007/s11202-009-0118-0
[21] Richter B., Dialgebren, Doppelalgebren und ihre Homologie. Diplomarbeit (1997)
[22] Schein B. M., Uspekhi Mat. Nauk 19 1 (115) pp 187– (1964)
[23] Schein B. M., Izv. Vyssh. Uchebn. Zaved. Mat. 1 (44) pp 168– (1965)
[24] Schein, B. M. (1989). Restrictive Semigroups and Bisemigroups. Technical Report. Fayetteville, Arkansas, USA: University of Arkansas, 1–23.
[25] Zhuchok A. V., Algebra Discrete Math. 3 pp 116– (2009)
[26] Zhuchok A. V., Free commutative dimonoids 9 (1) pp 109– (2010)
[27] DOI: 10.1007/s11253-011-0498-8 · Zbl 1246.08002 · doi:10.1007/s11253-011-0498-8
[28] Zhuchok A. V., Algebra Discrete Math. 12 (2) pp 112– (2011)
[29] Zhuchok A. V., Algebra Discrete Math. 11 (2) pp 92– (2011)
[30] DOI: 10.1007/s10469-011-9144-7 · Zbl 1259.08003 · doi:10.1007/s10469-011-9144-7
[31] Zhuchok A. V., Proc. Inst. Appl. Math. Mech. 22 pp 99– (2011)
[32] Zhuchok A. V., Visnyk Kyiv. Univ. Ser. Phis.-Math. Nauku 4 pp 7– (2011)
[33] Zhuchok A. V., Decompositions of free dimonoids 154 (2) pp 93– (2012)
[34] Zhuchok A. V., Free (r,rr)-dibands 15 (2) pp 295– (2013) · Zbl 1317.08004
[35] Zhuchok A. V., Prob. Phys. Math. Tech. 17 (4) pp 43– (2013)
[36] Zhuchok A. V., Algebra Discrete Math. 16 (2) pp 299– (2013)
[37] Zhuchok A. V., Quasigroups Relat. Syst. 21 (2) pp 273– (2013)
[38] Zhuchok A. V., Proceedings of Institute of Mathematics of NAS of Ukraine, Monograph, Kiev. (in Ukrainian) (2014)
[39] DOI: 10.1134/S0037446615050055 · Zbl 1336.08001 · doi:10.1134/S0037446615050055
[40] DOI: 10.1007/s00233-015-9743-z · Zbl 1384.08002 · doi:10.1007/s00233-015-9743-z
[41] DOI: 10.1007/s40863-016-0038-4 · Zbl 1384.20059 · doi:10.1007/s40863-016-0038-4
[42] Zhuchok Y. V., Algebra Discrete Math. 20 (2) pp 330– (2015)
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