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Journal : Jurnal Matematika

PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

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Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ̃ is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R´ can be defined a bijective mapping from R to R´ that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R´. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ̃  if there exists a subring R^0 of R^R ̃  such that R is isomorphic to R^0. Furthermore, regular ring R^R ̃  can be said as an extension of regular ring R.
PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ̃ is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R´ can be defined a bijective mapping from R to R´ that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R´. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ̃  if there exists a subring R^0 of R^R ̃  such that R is isomorphic to R^0. Furthermore, regular ring R^R ̃  can be said as an extension of regular ring R.
SEMIGRUP- INTRA-REGULAR DAN KETERKAITANNYA DENGAN BI-IDEAL,QUASI-IDEAL, SERTA IDEAL KANAN DAN KIRI Purwandani, Meiliana; Sumanto, YD
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

 . A -semigroup is generalization from semigroup, which concepts in -semigroup analogue with concepts in semigroup. is called a -semigroup if there is a mapping between two nonempty sets  and , written as , such that , for all  and . A -semigroup is said to be intra-regular if contains for all elements of intra regular, is if , for all  and . In this paper, discussed about intra-regular -semigroup and the relation based on bi-ideals, quasi-ideals, and ideals right and left. 
PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ? is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R' can be defined a bijective mapping from R to R' that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R'. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ?  if there exists a subring R^0 of R^R ?  such that R is isomorphic to R^0. Furthermore, regular ring R^R ?  can be said as an extension of regular ring R.
SEMIGRUP- INTRA-REGULAR DAN KETERKAITANNYA DENGAN BI-IDEAL,QUASI-IDEAL, SERTA IDEAL KANAN DAN KIRI Purwandani, Meiliana; Sumanto, YD
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

 . A -semigroup is generalization from semigroup, which concepts in -semigroup analogue with concepts in semigroup. is called a -semigroup if there is a mapping between two nonempty sets  and , written as , such that , for all  and . A -semigroup is said to be intra-regular if contains for all elements of intra regular, is if , for all  and . In this paper, discussed about intra-regular -semigroup and the relation based on bi-ideals, quasi-ideals, and ideals right and left. 
PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ? is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R' can be defined a bijective mapping from R to R' that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R'. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ?  if there exists a subring R^0 of R^R ?  such that R is isomorphic to R^0. Furthermore, regular ring R^R ?  can be said as an extension of regular ring R.