Generating subdirect products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

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Subdirect products of semirings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201003696 ◽

2001 ◽

Vol 26 (9) ◽

pp. 539-545

Author(s):

P. Mukhopadhyay

Keyword(s):

Distributive Lattice ◽

Subdirect Product ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Subdirect Products ◽

Necessary And Sufficient

Bandelt and Petrich (1982) proved that an inversive semiringSis a subdirect product of a distributive lattice and a ring if and only ifSsatisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the ring involved can be gradually enriched to a field. Finally, we provide a construction of fullE-inversive semirings, which are subdirect products of a semilattice and a ring.

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Direct and special subdirect products of division rings and of rings without divisors of zero

Siberian Mathematical Journal ◽

10.1007/bf00970118 ◽

1980 ◽

Vol 21 (1) ◽

pp. 38-46 ◽

Cited By ~ 3

Author(s):

R. Gonchigdorzh

Keyword(s):

Division Rings ◽

Subdirect Products

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Large subdirect products of flat modules

Communications in Algebra ◽

10.1080/00927879608825642 ◽

1996 ◽

Vol 24 (4) ◽

pp. 1389-1407 ◽

Cited By ~ 3

Author(s):

L. Oyonarte ◽

B. Torrecillas

Keyword(s):

Flat Modules ◽

Subdirect Products

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Subdirect products of rings and distributive lattices

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500016643 ◽

1982 ◽

Vol 25 (2) ◽

pp. 155-171 ◽

Cited By ~ 7

Author(s):

Hans-J. Bandelt ◽

Mario Petrich

Keyword(s):

Unary Operation ◽

General Construction ◽

Distributive Lattices ◽

Identity Mapping ◽

Additive Subgroup ◽

Binary Operations ◽

Subdirect Products

Rings and distributive lattices can both be considered as semirings with commutative regular addition. Within this framework we can consider subdirect products of rings and distributive lattices. We may also require that the semirings with these restrictions are regarded as algebras with two binary operations and the unary operation of additive inversion (within the additive subgroup of the semiring). We can also consider distributive lattices with the two binary operations and the identity mapping as the unary operation. This makes it possible to speak of the join of ring varieties and distributive lattices. We restrict the ring varieties in order that their join with distributive lattices consist only of subdirect products. In certain cases these subdirect products can be obtained via a general construction of semirings by means of rings and distributive lattices.

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On the finite presentation of subdirect products and the nature of residually free groups

American Journal of Mathematics ◽

10.1353/ajm.2013.0036 ◽

2013 ◽

Vol 135 (4) ◽

pp. 891-933 ◽

Cited By ~ 22

Author(s):

Martin R. Bridson ◽

James Howie ◽

Charles F. Miller ◽

Hamish Short

Keyword(s):

Free Groups ◽

Finite Presentation ◽

Subdirect Products

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On a cancellation rule for subdirect products of lattice ordered groups and of GMV-algebras

Mathematica Slovaca ◽

10.2478/s12175-007-0016-5 ◽

2007 ◽

Vol 57 (3) ◽

Cited By ~ 1

Author(s):

Ján Jakubík

Keyword(s):

Present Note ◽

Variety Of Algebras ◽

Subdirect Decomposition ◽

Ordered Groups ◽

Lattice Ordered Groups ◽

Subdirect Products

AbstractThe notion of internal subdirect decomposition can be defined in each variety of algebras. In the present note we prove the validity of a cancellation rule concerning such decompositions for lattice ordered groups and for GMV-algebras. For the case of groups, this cancellation rule fails to be valid.

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