# A reduction theorem for ring varieties whose subvariety lattice is distributive

Discussiones Mathematicae - General Algebra and Applications (2010)

- Volume: 30, Issue: 1, page 119-132
- ISSN: 1509-9415

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topMikhail V. Volkov. "A reduction theorem for ring varieties whose subvariety lattice is distributive." Discussiones Mathematicae - General Algebra and Applications 30.1 (2010): 119-132. <http://eudml.org/doc/276650>.

@article{MikhailV2010,

abstract = {We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.},

author = {Mikhail V. Volkov},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {variety of rings; subvariety lattice; distributive lattice; torsion-bounded variety; Mal'tsev product},

language = {eng},

number = {1},

pages = {119-132},

title = {A reduction theorem for ring varieties whose subvariety lattice is distributive},

url = {http://eudml.org/doc/276650},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Mikhail V. Volkov

TI - A reduction theorem for ring varieties whose subvariety lattice is distributive

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2010

VL - 30

IS - 1

SP - 119

EP - 132

AB - We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.

LA - eng

KW - variety of rings; subvariety lattice; distributive lattice; torsion-bounded variety; Mal'tsev product

UR - http://eudml.org/doc/276650

ER -

## References

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- [8] M.V. Volkov, Periodic varieties of associative rings, Izvestiya VUZ. Matematika no.8 (1979) 3-13 [Russian; Engl. translation Soviet Math., Izv. VUZ 23 (8) (1979), 1-12].
- [9] M.V. Volkov, Identities in lattices of ring varieties, Algebra Universalis 23 (1986), 32-43. doi: 10.1007/BF01190909 Zbl0607.17001
- [10] M.V. Volkov and A.G. Geĭn, Identities of almost nilpotent Lie rings, Mat. Sbornik 118 (1) (1982), 132-142 [Russian; Engl. translation Math. USSR, Sbornik 46 (1) (1983), 133-142]. Zbl0494.17009
- [11] E.I. Zel'manov, On Engel Lie algebras, Sibirsk. Mat. Zh 26 (5) (1988), 112-117 [Russian; Engl. translation Siberian Math. J. 29 (5) (1988), 777-781].
- [12] K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov and A.I. Shirshov, Rings that are nearly associative, Academic Press, New York 1982. Zbl0487.17001

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