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The Total Graphs of Finite Commutative Semirings

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2 Published in 2017 at "Results in Mathematics"

DOI: 10.1007/s00025-016-0595-y

Abstract: Anderson and Badawi (J Algebra 320(7):2706–2719, 2008) characterized all commutative rings having total graphs without any 3-cycles. In this paper we expand those results to the semiring setting and obtain the characterization of finite commutative… read more here.

Keywords: commutative semirings; total graphs; finite commutative; graphs finite ... See more keywords

Ideals and their complements in commutative semirings

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1 Published in 2019 at "Soft Computing"

DOI: 10.1007/s00500-018-3493-2

Abstract: We study conditions under which the lattice $${{\mathrm{\mathbf {Id}}}}\mathbf R$$IdR of ideals of a given a commutative semiring $${\mathbf {R}}$$R is complemented. At first we check when the annihilator $$I^*$$I∗ of a given ideal I… read more here.

Keywords: ideals complements; complements commutative; commutative semirings;