Associative Algebras with a Distributive Lattice of Subalgebras

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

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Compatible O-operators on bimodules over associative algebras

Journal of Algebra ◽

10.1016/j.jalgebra.2019.05.013 ◽

2019 ◽

Vol 532 ◽

pp. 80-118 ◽

Cited By ~ 2

Author(s):

Jiefeng Liu ◽

Chengming Bai ◽

Yunhe Sheng

Keyword(s):

Associative Algebras

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Congruence relations on almost distributive lattices-II

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500054 ◽

2019 ◽

pp. 2150005

Author(s):

Gezahagne Mulat Addis

Keyword(s):

Distributive Lattice ◽

Congruence Relation ◽

Congruence Class ◽

Distributive Lattices ◽

Ideal Formula ◽

Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

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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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