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Article . 2023
License: CC BY
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SSRN Electronic Journal
Article . 2023 . Peer-reviewed
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Article . 2023
License: CC BY
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Article . 2023
License: CC BY
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On Clean and Nil-clean Symbolic 2-Plithogenic Rings

Authors: P. Prabakara; Florentin Smarandache;

On Clean and Nil-clean Symbolic 2-Plithogenic Rings

Abstract

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2 − SPR.

Keywords

clean ring, Electronic computers. Computer science, symbolic 2-plithogenic ring, QA1-939, QA75.5-76.95, nil-clean ring, clean symbolic 2-plithogenic ring, nil-clean symbolic 2-plithogenic ring, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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