?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=NIL+DERIVATION+AND+%CE%B4-IDEAL+ON+POLYNOMIAL+RING&rft.creator=DITHA+%2C+LATHIFATUL+MURSYIDAH&rft.subject=510+Matematika&rft.description=Given+a+ring+R.+The+additif+mapping+d+%3A+R+%E2%86%92+R+is+called+derivation+if+d+satisfies%0D%0ALeibniz%E2%80%99s+rule%2C+i.e.%2C+d(ab)+%3D+d(a)b+%2B+ad(b)%2C+for+every+a%2C+b+%E2%88%88+R.+In+the+special+case%2C%0D%0Afor+each+x+%E2%88%88+R+there+exists+a+positive+integer+n+which+depends+on+x+such+that%0D%0An%0D%0Ad%0D%0A(x)+%3D+0%2C+the+mapping+d+is+called+as+a+nil+derivation+on+R.+The+concept+of+%CE%B4-ideal%0D%0Awhich+is+an+ideal+that+remains+stable+under+the+derivation+operation+%CE%B4.+The+research%0D%0Astarting+with+the+construction+of+nil+derivations+on+polynomial+rings%2C+followed+by+an%0D%0Ainvestigation+of+the+nilpotency+index+properties+of+nil+derivations.+Furthermore%2C+this%0D%0Astudy+discusses+the+relationship+between+nil+derivations+and+nilpotent+derivations%0D%0Aas+well+as+linear+combinations+of+nil+derivations.+Besides%2C+we+give+the+ilustration%0D%0Aexample+based+on+the+theorem+that+we+obtained.%0D%0AKeywords%3A+nil+derivation%2C+%CE%B4-ideal%2C+linear+combinations%2C+polynomial+ring.&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM&rft.date=2025-01-14&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84510%2F1%2FABSTRAK.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84510%2F2%2FSKRIPSI%2520FULL.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F84510%2F3%2FSKRIPSI%2520TANPA%2520BAB%2520PEMBAHASAN.pdf&rft.identifier=++DITHA+%2C+LATHIFATUL+MURSYIDAH++(2025)+NIL+DERIVATION+AND+%CE%B4-IDEAL+ON+POLYNOMIAL+RING.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F84510%2F