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Mat. Sb., 1994, Volume 185, Number 8, Pages 129–160 (Mi msb922)  

This article is cited in 31 scientific papers (total in 31 papers)

On the theory of epigroups. I

L. N. Shevrin

Ural State University

Abstract: Epigroups are viewed as unary semigroups with a pseudoinverse operation. Criteria are found for the existence of a partition of an epigroup into unipotent subepigroups, the inheritability of this property by all homomorphic images of an epigroup, and the decomposability of an epigroup into a band (semilattice) of Archimedean epigroups. Here, and in the second part of this paper to follow, the focus is on characterizations in terms of 'prohibited' objects, mainly epifactors, i.e., homomorphic images of subepigroups; attention is also paid to characterizations of the epigroups under consideration in the language of identities, and possible prospects for future investigations on varieties of epigroups are outlined.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 485–512

Bibliographic databases:

UDC: 512.531+512.532
MSC: Primary 20M10, 20M18; Secondary 20M07
Received: 15.10.1992

Citation: L. N. Shevrin, “On the theory of epigroups. I”, Mat. Sb., 185:8 (1994), 129–160; Russian Acad. Sci. Sb. Math., 82:2 (1995), 485–512

Citation in format AMSBIB
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\by L.~N.~Shevrin
\paper On the theory of epigroups.~I
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 8
\pages 129--160
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1302627}
\zmath{https://zbmath.org/?q=an:0839.20073}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 485--512
\crossref{https://doi.org/10.1070/SM1995v082n02ABEH003577}
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    This publication is cited in the following articles:
    1. L. N. Shevrin, “On the theory of epigroups. II”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 133–154  mathnet  crossref  mathscinet  zmath  isi
    2. Kelarev A., “Applications of Epigroups to Graded Ring-Theory”, Semigr. Forum, 50:3 (1995), 327–350  crossref  mathscinet  zmath  isi
    3. V. V. Butakov, L. M. Martynov, “Semigroups all of whose noncyclic subsemigroups are ideals”, Russian Math. (Iz. VUZ), 42:11 (1998), 90–92  mathnet  mathscinet  zmath  elib
    4. Zhil'tsov I., “The Free Archimedean Epigroups of Finite Degree”, Semigr. Forum, 57:3 (1998), 378–396  crossref  mathscinet  isi
    5. Pastijn F. Trotter P., “Complete Congruences on Lattices of Varieties and of Pseudovarieties”, Int. J. Algebr. Comput., 8:2 (1998), 171–201  crossref  mathscinet  zmath  isi
    6. Bogdanovic S., Ciric M., “Radicals of Green's Relations”, Czech. Math. J., 49:4 (1999), 683–688  crossref  mathscinet  zmath  isi
    7. Zhil'tsov I., “On Identities of Epigroups”, Dokl. Math., 62:3 (2000), 322–324  isi
    8. Ciric M., Bogdanovic S., “The Five-Element Brandt Semigroup as a Forbidden Divisor”, Semigr. Forum, 61:3 (2000), 363–372  crossref  mathscinet  zmath  isi
    9. Bogdanovic S., Ciric M., Popovic Z., “Semilattice Decompositions of Semigroups Revisited”, Semigr. Forum, 61:2 (2000), 263–276  crossref  mathscinet  zmath  isi
    10. Jackson M., “Finite Semigroups Whose Varieties Have Uncountably Many Subvarieties”, J. Algebra, 228:2 (2000), 512–535  crossref  mathscinet  zmath  isi
    11. Jackson M., “Small Inherently Nonfinitely Based Finite Semigroups”, Semigr. Forum, 64:2 (2002), 297–324  crossref  mathscinet  zmath  isi
    12. M. V. Volkov, I. A. Gol'dberg, “Identities of Semigroups of Triangular Matrices over Finite Fields”, Math. Notes, 73:4 (2003), 474–481  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. Bogdanovic S., Ciric M., Mitrovic M., “Semilattices of Nil-Extensions of Simple Regular Semigroups”, Algebr. Colloq., 10:1 (2003), 81–90  crossref  mathscinet  zmath  isi
    14. Mitrovic M., “On Semilattices of Archimedean Semigroups - a Survey”, Semigroups and Languages, eds. Araujo I., Branco M., Fernandes V., Gomes G., World Scientific Publ Co Pte Ltd, 2004, 163–195  crossref  mathscinet  zmath  isi
    15. Sapir O., “The Variety of Idempotent Semigroups Is Inherently Non-Finitely Generated”, Semigr. Forum, 71:1 (2005), 140–146  crossref  mathscinet  zmath  isi
    16. Mitrovic M., “Regular Subsets of Semigroups Related to their Idempotents”, Semigr. Forum, 70:3 (2005), 356–360  crossref  mathscinet  zmath  isi
    17. Yu Wang, Yingqin Jin, “Epigroups whose subepigroup lattice is 0-modular or 0-distributive”, Semigroup Forum, 2008  crossref  isi
    18. L. N. Shevrin, “Lattice properties of epigroups”, J. Math. Sci., 164:1 (2010), 148–154  mathnet  crossref  mathscinet  elib
    19. L. N. Shevrin, B. M. Vernikov, M. V. Volkov, “Lattices of semigroup varieties”, Russian Math. (Iz. VUZ), 53:3 (2009), 1–28  mathnet  crossref  mathscinet  zmath  elib
    20. Yu Wang, Yanfeng Luo, “Epigroups whose subepigroup lattices are meet semidistributive”, Algebra univers, 2009  crossref  mathscinet  isi
    21. Bogdanovic S., Popovic Z., Ciric M., “Bands of Lambda-Simple Semigroups”, Filomat, 24:4 (2010), 77–85  crossref  mathscinet  isi
    22. Bogdanovic S., Popovic Z., Ciric M., “Bands of K-Archimedean Semigroups”, Semigr. Forum, 80:3 (2010), 426–439  crossref  mathscinet  zmath  isi
    23. Skokov D.V., Vernikov B.M., “Chains and Anti-Chains in the Lattice of Epigroup Varieties”, Semigr. Forum, 80:2 (2010), 341–345  crossref  mathscinet  zmath  isi  elib
    24. Shouxu Du, Xinzhai Xu, K. P. Shum, “On Epiorthodox Semigroups”, International Journal of Mathematics and Mathematical Sciences, 2011 (2011), 1  crossref
    25. Bogdanovic S., Popovic Z., “Bands of Eta-Simple Semigroups”, Filomat, 26:4 (2012), 761–767  crossref  isi
    26. Jingguo Liu, “Epigroups in which the operation of taking pseudo-inverse is an endomorphism”, Semigroup Forum, 2013  crossref
    27. B. V. Novikov, “Non-commutative Grillet semigroups”, Algebra Discrete Math., 17:2 (2014), 298–307  mathnet  mathscinet
    28. D. V. Skokov, “Distributivnye elementy reshetki mnogoobrazii epigrupp”, Sib. elektron. matem. izv., 12 (2015), 723–731  mathnet  crossref
    29. B. M. Vernikov, D. V. Skokov, “Polumodulyarnye i dezargovy mnogoobraziya epigrupp. I”, Tr. IMM UrO RAN, 22, no. 3, 2016, 31–43  mathnet  crossref  mathscinet  elib
    30. D. V. Skokov, “Spetsialnye elementy nekotorykh tipov v reshetke mnogoobrazii epigrupp”, Tr. IMM UrO RAN, 22, no. 3, 2016, 244–250  mathnet  crossref  mathscinet  elib
    31. D. V. Skokov, “Cancellable elements of the lattice of epigroup varieties”, Russian Math. (Iz. VUZ), 62:9 (2018), 52–59  mathnet  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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