Indah Emilia Wijayanti
Jurusan Matematika FMIPA Universitas Gadjah Mada, Yogyakarta

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Pembentukan Ring Bersih Menggunakan Lokalisasi Ore Isnaini, Uha; Wijayanti, Indah Emilia
Jurnal Matematika dan Sains Vol 19 No 1 (2014)
Publisher : Institut Teknologi Bandung

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Abstract

Misalkan diberikan sebarang ring R (tidak harus komutatif) dan himpunan multiplikatif S Í R yang tidak memuat elemen nol. Lokalisasi Ore merupakan salah satu teknik pembentukan ring sehingga setiap elemen S memiliki invers di ring yang baru. Ring hasil lokalisasi tidak selalu mempertahankan sifat ring awal. Suatu ring sebarang dapat disisipkan ke  ring bersih, ring bersih-n dan ring peralihan. Pada paper ini akan dikaji sifat-sifat yang diperlukan untuk menyisipkan sebarang ring ke ring tersebut menggunakan lokalisasi. Kata kunci : Lokalisasi Ore, Elemen Satuan, Ring Bersih, Ring Peralihan, Ring Bersih-n.   Construction of Clean Ring using Ore Localization Abstract Let R be any ring (can be non commutative) and S Í R is a multiplicative set that does not contain any zero element. Ore localization is a powerful technique to construct a universal S-inverting ring. However the localization results do not always inherit properties of the first ring. An arbitrary ring can be inserted into the clean ring, n-clean ring, and exchange ring. Here, we show properties needed to insert any ring to the ring using localization. Keywords: Ore Localization, Unity, Clean Ring, Exchange Ring, n-Clean Ring.
MODUL τ[M]-INJEKTIVE Suprapto, Suprapto; Wahyuni, Sri; Wijayanti, Indah Emilia; Irawati, Irawati
Journal of Mathematics and Mathematics Education Vol 1, No 2 (2011): Journal of Mathematics and Mathematics Education
Publisher : Journal of Mathematics and Mathematics Education

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Abstract Let  R be a ring with unit and let  N be a left R-module. Then N is said linearly independent to  R (or N is R-linearly independent) if there is monomorphisma  By the definition of R-linearly independent, we may be able to generalize linearly independent relative to the R-module M. Module N is said M-linearly independent if there is monomorphisma .The module Q is said M-sublinearly independent if Q is a factor module of modules which is  M-linearly independent. The set of modules M-sublinearly independent denoted by  Can be shown easily that  is a subcategory of the category R-Mod. Also it can be shown that the submodules, factor modules and external direct sum of modules in  is also in the .The module Q is called P-injective if for any morphisma Q defined on L submodules of P can be extended to morphisma Q with , where  is the natural inclusion mapping. The module Q is called -injective if Q is P-injective, for all modules P in .In this paper, we studiet the properties and characterization of -injective. Trait among others that the direct summand of a module that is -injective also -injective. A module is -injective if and only if the direct product of these modules also are -injective. Key words : Q ()-projective, P ()-injective.
Setiap Modul merupakan Submodul dari Suatu Modul Bersih Sari, Kartika; Wijayanti, Indah Emilia
Jurnal Matematika Integratif Volume 11 No 1 (April 2015)
Publisher : Jurnal Matematika Integratif

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Abstract

Diberikan ring R dengan elemen satuan. Suatu ring R dikatakan bersih apabila setiap elemennya dapat dinyatakan dalam bentuk jumlahan suatu elemen unit dan suatu elemen idempoten dari ring R, sedangkan suatu R-modul M dikatakan bersih apabila ring endomorfismanya merupakan ring bersih. Berdasarkan sifat bahwa modul kontinu merupakan modul bersih, dalam penelitian ini ditunjukkan bahwa setiap modul merupakan submodul dari suatu modul bersih.
ON FREE IDEALS IN FREE ALGEBRAS OVER A COMMUTATIVE RING Wardati, Khurul; Wijayanti, Indah Emilia; Wahyuni, Sri
Journal of the Indonesian Mathematical Society Volume 21 Number 1 (April 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.1.170.59-69

Abstract

Let A be a free R-algebra where R is a unital commutative ring. An ideal I in A is called a free ideal if it is a free R-submodule with the basis contained in the basis of A. The denition of free ideal and basic ideal in the free R-algebra are equivalent. The free ideal notion plays an important role in the proof of some special properties of a basic ideal that can characterize the free R-algebra. For example, a free R-algebra A is basically semisimple if and only if it is a direct sum of minimal basic ideals in A: In this work, we study the properties of basically semisimple free R-algebras.DOI : http://dx.doi.org/10.22342/jims.21.1.170.59-69
OBYEK GRUP DAN OBYEK KOGRUP DARI SEBUAH KATEGORI Puspita, Nikken Prima; Wijayanti, Indah Emilia; Susanti, Yeni
MATEMATIKA Vol 13, No 2 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

. A category contained a classes of objects and morphism between  two object. For any chategory with initial object, terminal object, product and coproduct can defined a special object i.e group object and cogroup object. Object group obtained from cathegory object which have fulfil definition like definition a group. The cogroup object is dual from group object.  
ON Ï„ [M ]-COHEREDITARY MODULES Suprapto, S; Wahyuni, Sri; Wijayanti, Indah Emilia; Irawati, I
Jurnal ILMU DASAR Vol 12 No 2 (2011)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

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Abstract

Let R be a ring with unity and N a left R-module. Then N is said linearly independent to R (or N is R-linearly independent) if there exists a monomorphism ? : R(?) ? N . We can define a generalization of linearly independency relative to an R-module M. N is called M-linearly independent if there exists a monomorphism ?:M(?) ?N. Amodule  iscalled M-sublinearly independentif  is a factormodule of a module which is M-linearly independent. The set of M-sublinearly independent modules is denoted by ? [M ]. It is easy to see that ? [M ] is subcategory of category R-Mod. Furthermore, any submodule, factor module and external direct sum of module in ? [M ] are also in ? [M ]. A module is called ? [M ]-injective if it is P-injective, for all modules P in ? [M ]. Q is called ? [M ]-cohereditary if Q ?? [M ] and any factor module of Q is ? [M ]-injective. In this paper, we study the characterization of category ? [M ]-cohereditary modules. For any Q in ? [M ], Q is a ? [M ]-cohereditary if and only if every submodule of Q-projective module in ? [M ] is Q-projective. Moreover, Q is a ? [M ]-cohereditary if and only if every factor module of Q is a direct summand of module which contains this factor module. Also, we obtain some cohereditary properties of category ? [M ]. There are: for any R-modules P, Q. If Q is P-injective and every submodule of P is Q-projective, then Q is cohereditary (1); if P is Q-projective and Q is cohereditary, then every submodule of P is Q-projective (2); a direct product of modules which ? [M ]-cohereditary is ? [M ]-cohereditary (3). The cohereditary characterization and properties of category ? [M ] above is truly dual of characterization and properties of category ? [M ].
ON JOINTLY PRIME RADICALS OF (R,S)-MODULES Yuwaningsih, Dian Ariesta; Wijayanti, Indah Emilia
Journal of the Indonesian Mathematical Society Volume 21 Number 1 (April 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.1.199.25-34

Abstract

Let $M$ be an $(R,S)$-module. In this paper a generalization of the m-system set of modules to $(R,S)$-modules is given. Then for an $(R,S)$-submodule $N$ of $M$, we define $sqrt[(R,S)]{N}$ as the set of $ain M$ such that every m-system containing $a$ meets $N$. It is shown that $sqrt[(R,S)]{N}$ is the intersection of all jointly prime $(R,S)$-submodules of $M$ containing $N$. We define jointly prime radicals of an $(R,S)$-module $M$ as $rad_{(R,S)}(M)=sqrt[(R,S)]{0}$. Then we present some properties of jointly prime radicals of an $(R,S)$-module.DOI : http://dx.doi.org/10.22342/jims.21.1.199.25-34
ON FREE PRODUCT OF N-COGROUPS Wijayanti, Indah Emilia
Journal of the Indonesian Mathematical Society Volume 18 Number 2 (October 2012)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.18.2.116.101-111

Abstract

looked at pdf abstractDOI : http://dx.doi.org/10.22342/jims.18.2.116.101-111
PRIMENESS IN CATEGORY OF MODULES AND CATEGORY OF COMODULES OVER CORINGS Wijayanti, Indah Emilia
Journal of the Indonesian Mathematical Society Volume 14 Number 1 (April 2008)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.14.1.58.13-24

Abstract

We recall the notion of prie modules and use the analogue technique to define prime comodules and corings. Moreover, the related properties are of interest. We investigate the relation of primeness of C-comodule M and the dual algebra *C of a coring C, the relation to projectivity of a coring in the associated category, the implication of the primeness to the injective hull and product of prime coalgebras. DOI : http://dx.doi.org/10.22342/jims.14.1.58.13-24
On Fully Prime Radicals Wijayanti, Indah Emilia; Yuwaningsih, Dian Ariesta
Journal of the Indonesian Mathematical Society Volume 23 Number 2 (October 2017)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.23.2.302.33-45

Abstract

In this paper we give a further study on fully prime submodules. For any fully prime submodules we define a product called $\am$-product. The further investigation of fully prime submodules in this work, i.e. the fully m-system and fully prime radicals, is related to this product. We show that the fully prime radical of any submodules can be characterize by the fully m-system. As a special case, the fully prime radical of a module $M$ is the intersection of all minimal fully prime submodules of $M$.