Journal ArticleDOI
Some Remarks on the Jacobson Radical Types of Semirings and Related Problems
Le Hoang Mai,Nguyen Xuan Tuyen +1 more
TLDR
In this article, a semiring version of Snapper's Theorem is given for polynomial semirings over zerosum-free commutative semiirings.Abstract:
In this paper, we show that the J
s
-radical and the nil-radical of zerosumfree commutative semirings coincide. Based on this result, a semiring version of Snapper’s Theorem is given for polynomial semirings over zerosumfree commutative semirings, and zerosumfree commutative J
s
-semisimple semirings are completely described. Finally, Problem 1 in Katsov and Nam (Commun. Algebra 42: 5065–5099, 2014) is solved for semisimple, additively π-regular, and anti-bounded artinian semirings.read more
Citations
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Journal ArticleDOI
The jacobson radical types of Leavitt path algebras with coefficients in a commutative unital semiring
On the Jacobson radical and semisimplicity of a semiring
A. K. Bhuniya,Puja Sarkar +1 more
TL;DR: In this article , the authors introduce two Jacobson-type Hoehnke radicals, m-radical and s-radical, of a semimodule over a division semiring, and characterize every semisimple semiring as a subdirect product of primitive semirings.
References
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Book
A first course in noncommutative rings
TL;DR: In this article, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Book
Semirings and their Applications
TL;DR: In this paper, the authors define Hemirings and semirings as "sets and relations with values with values in a semiring" and define a set of conditions on semimodal construction.
Book
Rational Series and Their Languages
TL;DR: This chapter discusses the development of Rational Series over a Principal Ring, a model based on the model developed in Chapter I, and its applications to Languages and Codes.
Book
Automata-theoretic aspects of formal power series
Arto Salomaa,Matti Soittola +1 more
TL;DR: The style has sometimes been characterized as austere or severe, but the author does expect the reader to be able to fill in the more obvious details and the author permits him to present the leading ideas in an uncluttered way.
Journal ArticleDOI
On the definition of a family of automata
TL;DR: The definition of a family (~ of automata derived from the family a0 of the finite one-way one-tape automata is discussed, which is a very elementary modification of G0 and it is not.